Question

The ratio of the sum of n terms that 2APs is (7n+1)::4n+27) find the ratio of there $th terms .​

Answer 1

Step-by-step explanation:

n2(2a1+(n−1)d1)][n2(2a2+(n−1)d2)]=7n+14n+27

Cancelling common terms on the left hand side,

(2a1+(n−1)d1)(2a2+(n−1)d2)=7n+14n+27

Taking 2 common on both sides,

(a1+(n−1)2d1)(a2+(n−1)2d2)=7n+124n+272

(a1+(n−1)2d1)(a2+(n−1)2d2)=7n+14n+27...(equation1)

Now we have to find the ratio of 9th term, in mathematical terms we have to find,

(a1+8d1)(a2+8d2) equation 2

Look closely at equation 2 and equation number 1. In equation number 1, if

(n−1)2=8

n−1=16

n=17

Putting n=17 in equation number 1 we get,

(a1+8d1)(a2+8d2)=717+1417+27

(a1+8d1)(a2+8d2)=12095

Simplifying further we get,

(a1+8d1)(a2+8d2)=2419

which is the ratio of 9th term of the series.

PS: This is the first time I am using LaTex to write an answer. Feedback is appreciated.