Question

Find the number of terms in each of the following APs:

(i) $7,13,\mathrm{19....},205$

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

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

Answer 1

The correct option is A

34, 27

(i) $7,13,\mathrm{19....},205$

First term, $a=7$

Common difference, $d=13-7=6$

$a_n=205$

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

$205=7+(n-1)6$
$\Rightarrow 205=6n+1$

$\Rightarrow 204=6n$

$\Rightarrow n=\frac{204}{6}=34$

Therefore, there are 34 terms in the given arithmetic progression.

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

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

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

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

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

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