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The ratio of the sum of n terms of two A.P.s is (7n+1):(4n+27).Find the ratio of their mth term.
if 1+2+3+..............+n = 666, find the value of n.
The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last terms to the product of the two middle terms is 7 : 15. Find the numbers.
If the mth term of an A.P. be 1/n and nth term be 1/m, then show that its (mn)th term is 1.
Three alternate terms of an AP are x+y, x-y and 2x + 3y, then x =
a) -y
b) -2y
c) -4y
d) -6y
IF THE SUM OF FIRST m TERMS OF AN AP IS n. AND THE SUM OF FIRST n TERMS IS m, THEN SHOW THAT THE SUM OF ITS FIRST( m+n) TERMS IS -(m+n).
if 3x+k,2x+9 and x+13 are three consecutive terms of an AP.,Find k.
Maths Project :make designs using arithmetic progression
the sum of the two numbers is 25 and the reciprocals is 3/10. find the numbers
if the pth term of an A.P is q and the qth term is p, prove that its nth term is (p+q-n)
the sum of the first n terms of an AP is given by sn=3n2-n , determine the AP and its 25thterm.
If m times the mth term of an A.P is equal to n times its nth term, show that the (m+n)th term of the A.P is zero.
Find the LCM of (x + 3)(6x2 + 5x+ 4) and (2x2 + 7x + 3) (x + 3)
(2x + 1) (x + 3) (3x + 4)
(4x2 – 1) (x + 3)2 (3x + 4)
(4x2 – 1) (x + 3) (3x + 4)
(2x – 1) (x – 3) (3x + 4)
Hint:
the sum of first six terms of an ap is 42 .the ratio of its 10th term is and its 30th term is 1:3. calculate the first and thirteenth term
The sum of the third and seventh term of an A.P. is 6 and their product is 8. Find the sum of the first sixteen terms of the A.P. .
If pth , qth and rth term of an AP are a,b,c respectively , then show that
(a-b)r +(b-c)p + (c-a)q = 0
Please help me with this question asap .
the sum of the first n terms of an AP whose first term is 8 and difference is 20 is equal to sum of 2n terms of another AP whose first term is -30 and common difference is 9. Find the AP
150 workers were engaged to finish a piece of work in a certain no. of days. 4 workers droped d 2nd day, 4 more workers droped the 3rd day n so on..... it takes 8 more days to finish the work now ..find d no. of days in vch the work waz completed....
A body falls 8 m in the first second of its motion , 24 m in second, 40m in 3rd n so on . How long will it take to fall 2048 m. ??
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the
if 3 , 4+ 3, 6- p are in ap . then p must equal to :------
If the sum of first 7 terms of an AP is 49 and that of first 17 terms is 289.Find the sum of first n terms
The sum of n terms of two ap are in ratio (5n+4) : (9n+6) Find the ratio of their 18th term?
plzz reply with solution
the ratio of the sum of n terms of two AP's is (7n+1):(4n+27).find the ratio of their m th terms.
Answer: let a1 , a2 be the 1st terms and d1 , d2 the common differences of the two given A.P's. then the sums of their n terms are given by
Sn = n/2 {2.a1+(n-1)d1} and Sn' = n/2{2. a2 +(n-1)d2}
Sn/Sn' = n/2{2.a1+(n-1)d1} / n/2{2.a2 + (n-1)d2}
Sn / Sn' = 2.a1+(n-1)d1 / 2.a2 + (n-1)d2
it is given that
Sn / Sn' = 7n+1 / 4n + 27
2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7n+1 / 4n+27 ........................ (i)
To find the ratio of the mth terms of the two given AP's , we replace n by (2m-1) in equation (i)
therefore, 2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7(2m-1) + 1 / 4(2m-1) + 27
a1 + (m-1)d1 / a2 + (m-1)d2 = 14m - 6 / 8m + 23
Hence, the ratio of the mth terms of the two A.P's is (14m - 6) : (8m + 23)
My question is, why it has been assumed (2m-1) in the place of 'n' ? has it been arrived from solving with the help of a formula or is it a mere assumption? if it is simply an assumption, why it should be assumed as (2m-1) ? why not 2m or (m - 1)
If sn, the sum of first n terms of an AP is given by sn= (3n2-4n), then find its nth term.
Find the middle term (s) in the A.P. 20,16,12,.........-176.
If the sum of m terms of an A.P is the same as the sum of n terms of the same A.P, show that the sum of its (m+n) terms is zero.
what are the uses of arithmetic progressions in daily life? i want atmost 10, pls help me as soon as possible
if the nth term of an AP is (2n+1) find the sum of first n terms of the AP
sum of first p , q and r terms of an A.P. are a , b and c respectively. Prove that :
a/p (q-r) + b/p(r-p) + c/r (p-q) = 0
A lamp lighter has to light 100 gas lamps. He takes one and half minutes to go from one lamp post to the next. Each lamp burns 10 cubic feet of gas per hour. How many cubic feet of gas has been burnt by 8.30pm, if he lights the first/last lamp at 6pm
If S1 , S2 , S3 are the sum of n terms of three AP's the first term of each being unity and respective common diffrence being 1 , 2 , 3_ _ _ _ _. Prove that S1+S3= 2S2.
which term of an AP 3,15,27,39............ will 132 more than its 54th term
By 8pm all the party guests had arrived. By 9p a third of them had departed . By 10pm a third of those remaining had also departed. By 11pm the same happened again and a third of those remaining had also departed. After this only 8 guests still remained. How many guests arrived?
Divide 56 into 4 parts which are in AP such that hte ratio of product of extremes to the product of mean is 5 : 6? Hoping for a quick response......plz.....[ May be within Sunday ]
if sum of n terms of an AP 2n2 + 5n, then find its nth term.
In an AP,the sum of first n term is 3n2/2+13n/2
find its 25th term
solve the solution 1+4+7+10.............+x = 287
find all the integer which are equal to 11 time the sum of sum of their digits
if Sn denotes the sum of first n terms of an A.P., prove that S12=3(S8-S4).
A man save Rs. 400 more each years than he did the year before. If he saves Rs. 2000 in the first year after how mny years will his savings be more than Rs. 100000 altogether?
the sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. find the first 3 terms of the AP.
The sum of 5 numbers in an Ap is 30 & sum of their squares is 220. find the third tern-
*** Plzzzzz solve with all steps ***
Divide 32 into 4 parts which are in A.P. such that the product of extremes is to the product of means is 7:15.
30) the digits of a positive integer,having three digits are in A.P. and their sum is 15.the number obtained by reversing the digits is 594 less than the original number.find the number.
Find the sum of all the integers between 100 and 200 that are not divisible by 9
In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.
A contractor employed 150 labourers to finish a peice of work in a certain no. of days. 4 workers went away the second day, 4 more workers went away the third day and so on. If it took 8 more days to finish the work , find the no. of days in which the work was completed.
ANURAG.
The sum of n 2n 3n terms of an AP are S1 S2 S3 respectively. Prove that S3=3(S2-S1).
Find the sum of first five multiples of 3?
write the ap whose second term is 13 and the difference of the 4th term from the 8th term is 16.
Which term of AP:121,117,113,......., is its first negative term?
write an ap sum of whose first 9 terms is zero...
find the sum of all the natural numbers between 200 and 300 which are divisible by 4.
help plsss
Find the sum to n terms of the series 1/( 1 + 1^2 + 1^4) + 2/( 1 + 2^2 + 2^4) + 3/( 1 + 3^2 + 3^4) +......
urgent
The angles of a quadrilateral are in a.p. whose common difference is 10degree.Find the angles.
If there are (2n+1) terms in A.P,then prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n.
Find the 20th term from the last term of the AP 3, 8, 13, .....253.
If sn denotes the sum of n terms of AP whose common difference is d and first term is a, find sn-2sn-1+sn-2
Show that sum of an AP whose first term is a,the second term b and the last term c,is equal to (a+c)(b+c-2a)/2(b-a)..Plzzz i need hlpp!!!!
if the Pth term of an AP is Q and its Qth term is P then show that its (P+Q)th term is zero/
The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.
in an AP,the sum of first ten terms is -150 and the sum of its next ten terms is -550.Find the AP.
How many terms of A.P. 18,15,12,... are needed to give the sum 45? Explain the double answer.
What is the explaination for the double answer?
if sn denotes the sum of first n trems of an ap, prove that s12=3(s8-s4)
If the nth term of a G.P. be p, then show that the product of the first (2n-1) terms is p2n-1.
THE ANGLES OF A TRIANGLE ARE IN A.P.THE GREATEST ANGLE IS TWICE THE LEAST.FIND ALL THE ANGLES OF THE TRIANGLE.
the two opposite vertices of a square are (3,2)and (7,6) . find coordinates of other two vrtices.
E.g: 9876543210, 01112345678
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Syllabus
The ratio of the sum of n terms of two A.P.s is (7n+1):(4n+27).Find the ratio of their mth term.
if 1+2+3+..............+n = 666, find the value of n.
Q.1. What is the missing number in the pie below?
The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last terms to the product of the two middle terms is 7 : 15. Find the numbers.
If the mth term of an A.P. be 1/n and nth term be 1/m, then show that its (mn)th term is 1.
Three alternate terms of an AP are x+y, x-y and 2x + 3y, then x =
a) -y
b) -2y
c) -4y
d) -6y
IF THE SUM OF FIRST m TERMS OF AN AP IS n. AND THE SUM OF FIRST n TERMS IS m, THEN SHOW THAT THE SUM OF ITS FIRST( m+n) TERMS IS -(m+n).
if 3x+k,2x+9 and x+13 are three consecutive terms of an AP.,Find k.
Maths Project :make designs using arithmetic progression
the sum of the two numbers is 25 and the reciprocals is 3/10. find the numbers
if the pth term of an A.P is q and the qth term is p, prove that its nth term is (p+q-n)
the sum of the first n terms of an AP is given by sn=3n2-n , determine the AP and its 25thterm.
If m times the mth term of an A.P is equal to n times its nth term, show that the (m+n)th term of the A.P is zero.
Find the LCM of (x + 3)(6x2 + 5x+ 4) and (2x2 + 7x + 3) (x + 3)
(2x + 1) (x + 3) (3x + 4)
(4x2 – 1) (x + 3)2 (3x + 4)
(4x2 – 1) (x + 3) (3x + 4)
(2x – 1) (x – 3) (3x + 4)
Hint:
the sum of first six terms of an ap is 42 .the ratio of its 10th term is and its 30th term is 1:3. calculate the first and thirteenth term
The sum of the third and seventh term of an A.P. is 6 and their product is 8. Find the sum of the first sixteen terms of the A.P. .
If pth , qth and rth term of an AP are a,b,c respectively , then show that
(a-b)r +(b-c)p + (c-a)q = 0
Please help me with this question asap .
the sum of the first n terms of an AP whose first term is 8 and difference is 20 is equal to sum of 2n terms of another AP whose first term is -30 and common difference is 9. Find the AP
150 workers were engaged to finish a piece of work in a certain no. of days. 4 workers droped d 2nd day, 4 more workers droped the 3rd day n so on..... it takes 8 more days to finish the work now ..find d no. of days in vch the work waz completed....
A body falls 8 m in the first second of its motion , 24 m in second, 40m in 3rd n so on . How long will it take to fall 2048 m. ??
An AP consists of 37 terms. The sum of the three middle most terms is 225 and the
if 3 , 4+ 3, 6- p are in ap . then p must equal to :------
If the sum of first 7 terms of an AP is 49 and that of first 17 terms is 289.Find the sum of first n terms
The sum of n terms of two ap are in ratio (5n+4) : (9n+6) Find the ratio of their 18th term?
plzz reply with solution
the ratio of the sum of n terms of two AP's is (7n+1):(4n+27).find the ratio of their m th terms.
Answer: let a1 , a2 be the 1st terms and d1 , d2 the common differences of the two given A.P's. then the sums of their n terms are given by
Sn = n/2 {2.a1+(n-1)d1} and Sn' = n/2{2. a2 +(n-1)d2}
Sn/Sn' = n/2{2.a1+(n-1)d1} / n/2{2.a2 + (n-1)d2}
Sn / Sn' = 2.a1+(n-1)d1 / 2.a2 + (n-1)d2
it is given that
Sn / Sn' = 7n+1 / 4n + 27
2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7n+1 / 4n+27 ........................ (i)
To find the ratio of the mth terms of the two given AP's , we replace n by (2m-1) in equation (i)
therefore, 2.a1 + (n-1)d1 / 2.a2 + (n-1)d2 = 7(2m-1) + 1 / 4(2m-1) + 27
a1 + (m-1)d1 / a2 + (m-1)d2 = 14m - 6 / 8m + 23
Hence, the ratio of the mth terms of the two A.P's is (14m - 6) : (8m + 23)
My question is, why it has been assumed (2m-1) in the place of 'n' ? has it been arrived from solving with the help of a formula or is it a mere assumption? if it is simply an assumption, why it should be assumed as (2m-1) ? why not 2m or (m - 1)
If sn, the sum of first n terms of an AP is given by sn= (3n2-4n), then find its nth term.
Find the middle term (s) in the A.P. 20,16,12,.........-176.
If the sum of m terms of an A.P is the same as the sum of n terms of the same A.P, show that the sum of its (m+n) terms is zero.
what are the uses of arithmetic progressions in daily life? i want atmost 10, pls help me as soon as possible
if the nth term of an AP is (2n+1) find the sum of first n terms of the AP
sum of first p , q and r terms of an A.P. are a , b and c respectively. Prove that :
a/p (q-r) + b/p(r-p) + c/r (p-q) = 0
A lamp lighter has to light 100 gas lamps. He takes one and half minutes to go from one lamp post to the next. Each lamp burns 10 cubic feet of gas per hour. How many cubic feet of gas has been burnt by 8.30pm, if he lights the first/last lamp at 6pm
If S1 , S2 , S3 are the sum of n terms of three AP's the first term of each being unity and respective common diffrence being 1 , 2 , 3_ _ _ _ _. Prove that S1+S3= 2S2.
which term of an AP 3,15,27,39............ will 132 more than its 54th term
By 8pm all the party guests had arrived. By 9p a third of them had departed . By 10pm a third of those remaining had also departed. By 11pm the same happened again and a third of those remaining had also departed. After this only 8 guests still remained. How many guests arrived?
Divide 56 into 4 parts which are in AP such that hte ratio of product of extremes to the product of mean is 5 : 6? Hoping for a quick response......plz.....[ May be within Sunday ]
if sum of n terms of an AP 2n2 + 5n, then find its nth term.
In an AP,the sum of first n term is 3n2/2+13n/2
find its 25th term
solve the solution 1+4+7+10.............+x = 287
find all the integer which are equal to 11 time the sum of sum of their digits
if Sn denotes the sum of first n terms of an A.P., prove that S12=3(S8-S4).
A man save Rs. 400 more each years than he did the year before. If he saves Rs. 2000 in the first year after how mny years will his savings be more than Rs. 100000 altogether?
the sum of 4th and 8th terms of an AP is 24 and the sum of 6th and 10th terms is 44. find the first 3 terms of the AP.
The sum of 5 numbers in an Ap is 30 & sum of their squares is 220. find the third tern-
*** Plzzzzz solve with all steps ***
Divide 32 into 4 parts which are in A.P. such that the product of extremes is to the product of means is 7:15.
30) the digits of a positive integer,having three digits are in A.P. and their sum is 15.the number obtained by reversing the digits is 594 less than the original number.find the number.
Find the sum of all the integers between 100 and 200 that are not divisible by 9
In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the A.P.
A contractor employed 150 labourers to finish a peice of work in a certain no. of days. 4 workers went away the second day, 4 more workers went away the third day and so on. If it took 8 more days to finish the work , find the no. of days in which the work was completed.
ANURAG.
The sum of n 2n 3n terms of an AP are S1 S2 S3 respectively. Prove that S3=3(S2-S1).
Find the sum of first five multiples of 3?
write the ap whose second term is 13 and the difference of the 4th term from the 8th term is 16.
Which term of AP:121,117,113,......., is its first negative term?
write an ap sum of whose first 9 terms is zero...
find the sum of all the natural numbers between 200 and 300 which are divisible by 4.
help plsss
Find the sum to n terms of the series 1/( 1 + 1^2 + 1^4) + 2/( 1 + 2^2 + 2^4) + 3/( 1 + 3^2 + 3^4) +......
urgent
The angles of a quadrilateral are in a.p. whose common difference is 10degree.Find the angles.
If there are (2n+1) terms in A.P,then prove that the ratio of the sum of odd terms and the sum of even terms is (n+1):n.
Find the 20th term from the last term of the AP 3, 8, 13, .....253.
If sn denotes the sum of n terms of AP whose common difference is d and first term is a, find sn-2sn-1+sn-2
Show that sum of an AP whose first term is a,the second term b and the last term c,is equal to (a+c)(b+c-2a)/2(b-a)..Plzzz i need hlpp!!!!
if the Pth term of an AP is Q and its Qth term is P then show that its (P+Q)th term is zero/
The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.
in an AP,the sum of first ten terms is -150 and the sum of its next ten terms is -550.Find the AP.
How many terms of A.P. 18,15,12,... are needed to give the sum 45? Explain the double answer.
What is the explaination for the double answer?
if sn denotes the sum of first n trems of an ap, prove that s12=3(s8-s4)
If the nth term of a G.P. be p, then show that the product of the first (2n-1) terms is p2n-1.
THE ANGLES OF A TRIANGLE ARE IN A.P.THE GREATEST ANGLE IS TWICE THE LEAST.FIND ALL THE ANGLES OF THE TRIANGLE.
the two opposite vertices of a square are (3,2)and (7,6) . find coordinates of other two vrtices.