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 'm'th terms.

Answer 1

Ratios of the sums of first n terms of AP is
(7n+1):(4n+27)

(2a+(n-1)d) : (2a' + (n-1)d') = (7n+1) : (4n+27) ----(1)

Let's consider the ratios of these two AP's (m)th term is

a(m) : a'(m)--------(2)

AP formula for (n)th term is a(n) = a+(n-1)d


Hence equation 2 became

a(m):a'(m)

= (2a + (2m-1)d) : (2a' + (2m-1)d')

by simplifying we will get

S(2m-1) : S'(2m-1)

now putting the values.

= (7(2m-1)+1) : (4(2m-1)+27) from equation 1

by simplifying

(14m-6) : (8m+23)

It's our answer.

The ratios of (m) th term of two APs is

(14m-6) : (8m+23)