Question

The $6^{th}$ and ${17}^{th}$ terms of an AP are $19$ and $41$ respectively, find the ${40}^{th}$ term.

• A. $87$
• B. $77$
• C. $85$
• D. $89$

Answer 1

The correct option is A $87$

Let $a$ and $d$ be the first term and the common difference of the given AP respectively. Then,
$a_6=19\Rightarrow a+5d=19$ $...\left(1\right)$
$a_{17}=41\Rightarrow a+16d=41$ $...\left(2\right)$
On subtracting $\left(2\right)$ from $\left(1\right),$ we get
$11d=22\Rightarrow d=2$
Putting $d=2$ in $\left(1\right),$ we get
$a=19-5\times 2=9$
Now, $a_{40}=a+39d=9+39\times 2=87$