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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.

^{2 }: n^{2.}show that the ratio of the m^{th}and n^{th}terms is (2m-1) : (2n-1)^{2}/2 + 5n/2, find its 25^{th }term.the sum of the two numbers is 25 and the reciprocals is 3/10. find the numbers

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 m

^{th}term of an A.P. be 1/n and n^{th}term be 1/m, then show that its (mn)^{th}term is 1.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).

Answer given:1050+1260-300=2010

Please explain with working.

Maths Project :make designs using arithmetic progression

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 s

_{n}=3n^{2}-n , determine the AP and its 25^{th}term.Find the first positive term of the A.P: -11, -8, -5,.......

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.

90.: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

what is te first negative term of AP:-17,-14,-11,............?

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 .

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....

t

_{n}= n^{2}, where n is even andt

_{n}= n^{2}- 1 , where n is oddAn AP consists of 37 terms. The sum of the three middle most terms is 225 and the

the nth term of an AP is given by a

_{n}= 4n - 5,then find the sum of first 25 terms of the AP.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

Pure and Ashu live in two different villages 165 km apart.They went to meet each other but there is no fast means of transport.Pure travels 15 km the first day,14 km on second day,13 km on third day and so on.Anshu travels 10 km the first day,12 km on second day,14 km on third day and so on.After how many days will they meet ?

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

Q.Find the common difference of an A.P in which ${a}_{16}-{a}_{12}=16$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 s

_{n}, the sum of first n terms of an AP is given by s_{n}= (3n^{2}-4n), then find its nth term.FIND the 4th term from the end of the A.P. ................ 2 , 5 , 8 ................ , 35If 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

Find the middle term (s) in the A.P. 20,16,12,.........-176.

if the nth term of an AP is (2n+1) find the sum of first n terms of the AP

Find the no. of multiples of 6 lying between 75 and 750.

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

the next term of the AP root 27,root 48,root 75,.............is:?

If S

_{1}, S_{2}, S_{3}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 S_{1}+S_{3}= 2S2.Third term of an A.P is 17 and the 10

^{th}term is 50 less than the 20^{th}term. Form the A.Pwhich term of an AP 3,15,27,39............ will 132 more than its 54

^{th}termThree alternate terms of an AP are x+y, x-y and 2x + 3y, then x =a) -yb) -2yc) -4yd) -6yDivide 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 ]

For the A.P -3, -7, -11,..... can we directly find a

_{30}- a_{20}without actually finding a_{30}and a_{20}? Give reasons for your answer.if sum of n terms of an AP 2n

^{2}+ 5n, then find its n^{th}term.if 3x+k,2x+9 and x+13 are three consecutive terms of an AP.,Find k.In an AP,the sum of first n term is 3n2/2+13n/2

find its 25th term

18th term of an ap is 30 more than its 8th term.of 15th term of the ap is 48,find the ap.

solve the solution 1+4+7+10.............+x = 287

390 plants are to be planted in a garden in a no. of rows. there are 40 plants in the first row, 38 plants in the second row, 36 plants in 3rd row and so on.in how many rows the 390 plants are planted? find the no.of plants in the last row.

if Sn denotes the sum of first n terms of an A.P., prove that S12=3(S8-S4).

A student taking test consisting of 10 quetions is told that each after the first is worth 2 mks more than the preceding ques. If 3rd ques. of the test is worh 5 mks..,what is the maximum score that the student can obtain by attempting 8 questions.

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.

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.

how many terms of an AP must be taken for their sum to be equal to 120 if its third term is 9 and the difference between the seventh and second term is 20

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.

(i) She can pay a lumpsum amount of Rs 2200000.

(ii) She can pay Rs 400000 cash and balance in 18 annual instalments of Rs 100000 plus 10% interest on the unpaid amount.

She prefers the option (i) and donates 50% of the difference of the costs in the above two options to national Relief Fund.

(a) What amount was donated to National Relief Fund?

(b) By choosing to pay a lumpsum amount and donating 50% of the difference to national Relief Fund. Which value is depicted by Mamta?

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) 2n + 5

(b) 2n - 5

(c) 8 - 3n

(d) 3n - 8

A

contractoremployed150 labourersto finish a peice of work in a certain no. of days.4 workerswent away thesecond day,4 more workerswent away thethird dayandso on. Ifit took 8 more daysto 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).

how many terms of an AP 5,8,11,..... add upto 670

Find the sum of first five multiples of 3?

Which term of AP:121,117,113,......., is its first negative term?

EXPERTS,

Jobanpreet applied for a teaching job got selected. She has been offered the job with a starting monthly salary of RS. 12500 with an annual increment of RS. 1250 .Find her salary after 15 years of service .Also, find the total amount received by her in 15 years.

find the sum of all the natural numbers between 200 and 300 which are divisible by 4.

help plsss

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.

Q) The sum of the first five terms of an AP is 25 and the sum of its next five terms is -75.Find the 10th term of the AP?

Q)In an AP the first term is 8 and the common difference is 7.If the last term of the AP is 218,find its middle term?

If s

_{n }denotes the sum of n terms of AP whose common difference is d and first term is a, find s_{n}-2s_{n-1}+s_{n-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!!!!

The nth term of an AP: a, a + d, a+2d, . . . . . . . is tn = . . .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/

Q.135. If a

_{1}, a_{2}, a_{3}, .... is an arithmetic progression with common difference 1 and $\sum _{\text{i=1}}^{98}{\text{a}}_{1}\text{=137,}\phantom{\rule{0ex}{0ex}}$ then the value of a_{2}+ a_{4}+ a_{6}+ ......+ a_{98}is(1) 67

(2) 83

(3) 93

(4) 98

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.

if sn denotes the sum of first n trems of an ap, prove that s12=3(s8-s4)

Which term of the sequence 7.3, 6.9, 6.5, 6.1, .... is the first negative term?

THE ANGLES OF A TRIANGLE ARE IN A.P.THE GREATEST ANGLE IS TWICE THE LEAST.FIND ALL THE ANGLES OF THE TRIANGLE.