Question

If $n^{th}$ terms of two A.P.s are $3n+8$ and $7n+15$, then the ratio of their ${12}^{th}$ terms will be:

• A. $\frac{4}{9}$
• B. $\frac{7}{16}$
• C. $\frac{3}{7}$
• D. $\frac{8}{15}$

Answer 1

The correct option is A

$\frac{4}{9}$

Explanation for the correct option

Step 1: Solve for ${12}^{th}$ terms

Given $n^{th}$ terms of two A.P.s are $t_n=3n+8$ and $t{\text{'}}_n=7n+15$

$\begin{array}{cccccc}\therefore & t_{12}& =& 3\left(12\right)+8& =& 44\\ & t{\text{'}}_{12}& =& 7\left(12\right)+15& =& 99\end{array}$

Step 2: Solve for the ratio of ${12}^{th}$ terms

$\frac{t_{12}}{t{\text{'}}_{12}}=\frac{44}{99}=\frac{4}{9}$

Hence the correct option is option(A)