Question

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

Answer 1

we know
Sn=n/2 {2a+(n-1) d}
so, we convert above in standard form

Sn/S"n=(7n+1)/(4n+27)

=n/2 {2.(4)+(n-1)7}/n/2 {2.(31/2)+(n-1)
4}

hence for Sn
first term =4 and common difference=7
for S"n
first term =31/2
common difference =4

now ,
Tn/T"n={4+(n-1) 7}/{31/2+(n-1) 4}

=(7n-3)/(31/2+4n-4)

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