Question

The ratio of the sum of n terms of two A.P's is (7n+1):(4n+27). Find the ratio of their m th terms.

Answer 1

Ratio of sum of n terms of two Ap's be Sn1/Sn2 = (7n+1)/(4n+27)
n/2[2a1+(n-1)d1]/n/2[2a2+(n-1)d2]=(7n+1)/(4n+27)

simplify it u get

[a1+(n-1)d1/2]/[a2+(n-1)d2/2]=(7n+1)/(4n+27)

put n=

Answer 2

Let a1,a2 be the first term and d1 and d2 the common differences of two given A.P's .

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

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

Sn/Sn' = n/2{2a+(n-1)d1}/ n/2{ 2a+(n-1)d2}

= 2a+(n-1)d1/ 2a+(n-1)d2

Given===== Sn/Sn'= 7n+1/4n+27

2a+(n-1)d1/2a+(n-1)d2 = 7n+1/4n+27--(1)

Replacing n by 2m-1

2a1+ (2m-2)d2/2a2+(2m-2)d2= 7(2m-1)+1/4(2m-1)+27

= a1+ ( m-1)d1 / a1+(m-1)d2=14m-6/8m+23

Ratio of mrh term == 14m-6 : 8m+23