Question

The $1^{st},2^{nd}$ and the last terms of an arithmetic progression are $5,9$ and $101$ respectively, What are the number of terms in the A.P.?

• A. $30$
• B. $50$
• C. $25$
• D. $75$

Answer 1

Answer: (C)

$25$

Given:

First term $=a=5$

Second term $=a+d=9$

$\Rightarrow d=9-5=4$

$a_n=a+(n-1)d=101$

$\Rightarrow 5+(n-1)4=101$

$\Rightarrow (n-1)4=96$

$\Rightarrow (n-1)=\frac{96}{4}=24$

$\Rightarrow n=25$ (Ans $\to$ C)