Question

If the ratio of the sum of first n term of two A.P is (7n +1): (4n + 27) find the ratio of their Mth term​

Answer 1

Answer:

Give any four examples of Male Dominated Social Structure of France from the lesson 'Joan of Arc.'

Answer 2

Answer:

Let a1, a2 be the first 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=2n[2a1+(n−1)d1]

And,

Sn′=2n[2a2+(n−1)d2]

Therefore,

Sn′Sn=2n[2a2+(n−1)d2]2n[2a1+(n−1)d1]=2a2+(n−1)d22a1+(n−1)d1

⟹2a2+(n−1)d22a1+(n−1)d1=4n+277n+1     ....(1)

To find the ratio of the mth terms of the two given AP's, we replace n by (2m-1) in equation 1.

Therefore,

2a2+(2m−2)d22a1+(2m−2)d1=4(2m−1)+277(2m−1)+1

⟹a2+(m−1)d2a1+(m−1)d1=8m+2314m−6

Hence, the ratio of the mth terms of two AP's is (14m−6):(8m+23).

Step-by-step explanation:

PLEASE MARK AS BRANILST AND LIKE