Question

Find the number of terms in an arithmetic progression for which the first term is $4$, last term is $22$ and the common difference is $\frac{1}{4}$

• A. $70$
• B. $71$
• C. $72$
• D. $73$

Answer 1

The correct option is D $73$

Let $a$ be the first term and $d$ be their common difference of the AP.
Then, $nth$ term of the AP$,T_n=a+(n-1)d$
Here, in the given AP,. $a=4;d=\frac{1}{4}$
Given
$T_n=22$
$\Rightarrow 4+(n-1)\times \frac{1}{4}=22$
$\Rightarrow (n-1)\times \frac{1}{4}=18$
$\Rightarrow n-1=72$
$n=73$
Hence there are $73$ terms in the series .