Question

If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.

Answer 1

Question :-

If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.

Solution :-

Sn = n/2 {a1 + (n - 1)d1}

Sn' = n/2 { a2 + (n - 1) d2}

a1 + (n - 1) d1 / a2 + (n - 1) d2 = 7n + 1 / 4n + 27

In order to find nth term, we have to replace n by 2m - 1

a1 + (2m - 1) d1 / a2 +(2m -1)/ d2

= 7(2m - 1) + 1/ 4(2m -1) + 27

= 14m - 7 + 1/ 8m - 4+27

= 14m - 6/ 8m + 23

Now replace m by 9 to get the ratio of 9th term

= 14(9) - 6/ 8(9) + 23

= 120/95

= 24/19.

Notebook solution : Click to the attachment.