Question

Find the number of terms in the following AP: $18,\frac{31}{2},13,...-47$

• A. 34,27
• B. 26,35
• C. 27,34
• D. 35,26

Answer 1

The correct option is A

34,27

Given AP is

$18,\frac{31}{2},13,...-47$

First term, $a=18$

Common difference, $d=\frac{31}{2}-18=-\frac{5}{2}$

$a_n$ =−47

Using formula $a_n=a+(n-1)d$ to find $n^{th}$ term of arithmetic progression, we get

$-47=18+(n-1)[-\frac{5}{2}]$

$\Rightarrow -94=36-5n+5$

$\Rightarrow 5n=135$
$\Rightarrow n=\frac{135}{5}=27$

Therefore, there are 27 terms in the given arithmetic progression.