Question

if the ratio of the sum of first n terms of two A.P 's is ( 7n + 1 ) : ( 4n + 27 ) , find the ratio of their mth term

Answer 1

Sn/sn =7n+1/4n+27 (given)

Where Sn is sum of n terms of 1st AP and sn is sum of n terms of second AP.

Sn =n/2(2A +(n-1)D) (A =first term, D =common difference) (Sum of AP formula)

sn=n/2(2a+(n-1)d) (a=first term, d=common difference) (Sum of AP formula)

Sn/sn=(2A+(n-1)D)/(2a+(n-1)d)

7n+1 /4n+27 = (2A+(n-1)D) / (2a+(n-1)d)

As, we have to find ratio of their 9th term, let n =2(9)-1=17

So, equation=>

7(17)+1/4(17)+27=2A+(16D)/2a+16d

120/95 =A+8D /a+8d

So, T9/t9 =120/95=24/