Question

The $21st$ term of the A.P. whose first two terms are $-3$ and $4$ is

• A. $17$
• B. $137$
• C. $143$
• D. $-143$

Answer 1

The correct option is B

$137$

Step 1: Find the common difference of given A.P

We know that the $nth$ term of an AP is given by the formula

$a_n=a+(n–1)d$

where, $a$ is the first term, $a_n$ is the n^th term, $d$ is the common difference

According to the question, we get

First-term, $a=–3$

Common difference,$d=4-(-3)=4+3=7$

Step 2: Find the $21st$ term of given A.P

Number of terms, $n=21$

On substituting the values in the above formula, we get

$a_{21}=–3+(21–1)7$

$a_{21}=–3+20\times 7$

$a_{21}=–3+140=137$

Therefore, the $21st$ term of the given A.P. is $137$

Hence, the correct option is B