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.

1. The ratio of the sums of m and n terms of an AP is m² : n^2. show that the ratio of the m^th and n^th terms is (2m-1) : (2n-1)
2. In an AP, the sum of first n terms is 3n²/2 + 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.

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.

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 s_n=3n²-n , determine the AP and its 25^thterm.

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)

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

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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 :------

1. 0
2. 2 / 3
3. 1 / 3
4. - 1/3

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 s_n, the sum of first n terms of an AP is given by s_n= (3n²-4n), then find its nth term.

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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

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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 ]

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*** 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.

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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.

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