Question

The ratio between the sum of n terms of two A.P.s is $3n+8:7n+15.$ Then the ratio between their ${12}^{th}$ terms is-

• A. 5:7
• B. 7:16
• C. 12:11
• D. None

Answer 1

Answer: (B)

7:16

$\frac{S_n}{S_n^{\prime }}=\frac{\left(n/2\right)[2a+(n-1\left)d\right]}{\left(n/2\right)[2a^{\prime }+(n-1\left)d^{\prime }\right]}=\frac{3n+8}{7n+15}$

or $\frac{a+\left(\frac{n-1}{2}\right)d}{a^{\prime }+\left(\frac{n-1}{2}\right)d^{\prime }}=\frac{3n+8}{7n+15}$ ....(i)

We have to find $\frac{T_{12}}{T_{12}^{\prime }}=\frac{a+11d}{a^{\prime }+11d^{\prime }}$

Choosing $(n-1)/2=11$ or $n=23$ in (i)

We get, $\frac{T_{12}}{T_{12}^{\prime }}=\frac{7}{16}$