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.

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.

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).

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

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

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

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

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

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.

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.

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

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a/p (q-r) + b/p(r-p) + c/r (p-q) = 0

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A B set out to meet each other from two places 165 km apart. 'A' travels 15 km the first day, 14 the second day, 13 the third day and so on. 'B' travels 10 Km the first day, 12 Km the second day, 14 the third day and so on. After how many days they will meet each other.

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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.

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help plsss

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*** Plzzzzz solve with all steps ***

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How many terms of an A.P: -6, -11/2, -5 ...... are needed to get the sum -25 ?

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 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

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