Question

If the sum of n terms of two A.P.’s are in the ratio (3n + 2) : (2n + 3), find the ratio of their 12^th terms.

Answer 1

Here,

\(\frac{S_n}{S'_n}\) = \(\frac{3n+2}{2n+3}\)

Now, we want to find ratio of 12^th term,

From (1) and (2)we get n-1 = 22 

i.e,

n = 23

∴ \(\frac{a_{12}}{a'_{12}}\) = \(\frac{3(23)+2}{2(23)+3}\)

= \(\frac{71}{49}\)