Question

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

• A. 5 : 7
• B. 7 : 16
• C. 12 : 11
• D. 11:12

Answer 1

The correct option is B

7 : 16

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

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 $\frac{(n-1)}{2}$ = 11 or n = 23 in (i), we get,

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