Question

The sum of n terms of two A.P. are in the ratio 5n+4:9n+6.
The ratio of their 18th terms is

• A. 47:84
• B. 179:321
• C. 89:159
• D. 2:3

Answer 1

The correct option is B 179:321

Let the sum of nth terms of two AP be denoted by $s_n$ and $S_n$. The first term and common difference of two AP's be denoted by a & d and A & D respectively
$s_n:Sn=(5n+4):(9n+6)$
$\Rightarrow \frac{\frac{n}{2}(2a+(n-1\left)d\right)}{\frac{n}{2}(2A+(n-1\left)D\right)}$$=\frac{5n+4}{9n+6}$
$\Rightarrow \frac{(2a+(n-1\left)d\right)}{(2A+(n-1\left)D\right)}$$=\frac{5n+4}{9n+6}$
Dividing numerator and denominator by 2
$\Rightarrow \frac{a+\frac{(n-1)d}{2}}{a+\frac{(n-1)D}{2}}=\frac{5n+4}{9n+6}$.......(i)