Question

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

Answer 1

we know formula,
Sn=n/2{2a+(n-1)d}

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

=n/2{2.4+(n-1)7}/n/2{2.31/2+(n-1)4}

here you see this is in the standard form
now for Sn
first term=4
common duffference=7
for S"n
first term=31/2
common difference=4
now,
Tn/T"n={4+(n-1)7}/{31/2+(n-1)4}

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