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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 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.Please show all calculations

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.How many 3 digit numbers are such that when divided by 7, leave a remainder 3 in each case.

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).

is

(a) -955

(b) -945

(c) -950

(d) -965

Maths Project :make designs using arithmetic progression

(a) 2n + 5

(b) 2n - 5

(c) 8 - 3n

(d) 3n - 8

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)

find the sum of n terms of the series (a+b) + (a

^{2}+2b) + (a^{3}+ 3b = .....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.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.

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

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....

Find the sum of first 15 terms of an AP whose nth term is 9-5n

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the

^{n}c_{1,}^{n}c_{2 }and^{n}c_{3}will be in arithmetic progression?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

if 3x+k,2x+9 and x+13 are three consecutive terms of an AP.,Find k.terms is 50. Find the A.P.

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)

_{1}, A_{2}are two AMs between two numbers a and b, then (2A_{1}- A_{2}) ( 2A_{2}- A_{1}) is equal to(A) a + b (B) $\frac{ab}{a+b}$ (C) ab (D) $\frac{a+b}{ab}$

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.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.

The sum of the first n terms of an AP is (3n

^{2}+ 5n). Which term of the AP is 152?what are the uses of arithmetic progressions in daily life? i want atmost 10, pls help me as soon as possible

Answer given:1050+1260-300=2010

Please explain with working.

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

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

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.which term of an AP 3,15,27,39............ will 132 more than its 54

^{th}termDivide 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 ]

whch one of the following is not an AP:

(A)13,8,3,-2,-7,-12

(B) 10.8,11.2,11.6,12,12.4

(C) 81/7,18 2/7,28 3/7,48 4/7,58 5/7

(D) 8 3/23,11 6/23,14 9/23,17 12/23

if sum of n terms of an AP 2n

^{2}+ 5n, then find its n^{th}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

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

find the sum of all three digit natural numbers divisible by 7????

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 7th term of an AP is 32 and its 13th term is 62. find 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.

The sum of the first 77 terms of an arithmetic progression is the same as the sum of its first 99 terms.

What will be the sum of its first 176 terms?

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.The sum of n terms of two AP are in the ratio (2n+3):(6n+5),then the ratio of their 13th terms is

(a) 53:155

(b)29:83

(c) 31:89

(d)27:8

Please answer with complete steps and explanation.

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.If a, b, c are in AP then a

^{3}+4b^{3}+c^{3}is equal to???????The sum of n 2n 3n terms of an AP are S1 S2 S3 respectively. Prove that S3=3(S2-S1).

Find the LCM of (x + 3)(6x

^{2}+ 5x+ 4) and (2x^{2}+ 7x + 3) (x + 3)(2x + 1) (x + 3) (3x + 4)

(4x

^{2}– 1) (x + 3)^{2}(3x + 4)(4x

^{2}– 1) (x + 3) (3x + 4)(2x – 1) (x – 3) (3x + 4)

Hint:Find the sum of first five multiples of 3?

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?

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

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

help plsss

If Sn denotes the sum of n terms of an AP and if S1= 6 , S7 = 105 , then show that Sn : S(n-3) = (n+3) : (n-3)

The angles of a quadrilateral are in a.p. whose common difference is 10degree.Find the angles.

find x so that 2x+1, x

^{2}+x+1&3x^{2}- 3x+ 3 are the consecutive terms of an A.P.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.

find 5th term from end of the AP 17,14.11............ -40

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 is given by a

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

find the 6th term from the end of the AP 5,2, -1 , -4................. -31 .

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.

Let

Tbe the_{r}th term of an A.P. IfrmT=_{m}nT_{n}, then show thatT= 0_{m+n}if sn denotes the sum of first n trems of an ap, prove that s12=3(s8-s4)

prove that S

_{n }- S_{n-1 }= a_{n}THE ANGLES OF A TRIANGLE ARE IN A.P.THE GREATEST ANGLE IS TWICE THE LEAST.FIND ALL THE ANGLES OF THE TRIANGLE.