Question

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

Answer 1

the ratio of the sum of 1st n term of two ap series is ( 7n+1):(4n+27)
let, a & a' be the 1st terms of two ap series and d&d' r common differences.
hence, 2a+(n-1) wd/2a'+(n-1)d'= ( 7n+1):(4n+27)
if n=1
a/a'=8/31....1no
and when n=2
then 2a+d/2a'+d'=15/35...2no
when n=9
then 2a+8d/2a'-8d'=64/63...3no
solving them u get a= 8, a'=31, d=14,d'=8
so their ratio of 9th terms=a+8d/a'+8d'=24/19=24:19