Question

If the n${}^{th}$ term of two AP's 63, 65, 67 .... and 3, 10, 17, .... is equal, then find the value of 'n'.

• A. 13
• B. 11
• C. 12
• D. 14

Answer 1

The correct option is A

13

Given, series are 63, 65, 67..... and 3, 10, 17......

Using formula n${}^{th}$ term of an AP $a_n=a+(n-1)d$
For the series 63, 65, 67....... n${}^{th}$ term is:

$a_n=63+(n-1)\left(2\right)$...............(1)

For the series 3, 10, 17.... n${}^{th}$ term is
$a_n=3+(n-1)\left(7\right)$.................(2)

$\because$ n${}^{th}$ term of both AP's are equal
$\Rightarrow 63+(n-1)\left(2\right)=3+(n-1)\left(7\right)$
$\Rightarrow 63+2n-2=3+7n-7$
$\Rightarrow 65=5n$
$\Rightarrow n=\frac{65}{5}=13$

Therefore, ${13}^{th}$ terms of both the APs are equal.