Question

If the $n^{th}$ term of an A.P. is $4n+1$, then the common difference, $d$ is equal to

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

Answer: (B)

$4$

The $n^{th}$ term of an A.P, whose first terms is $a$ and common difference is $d$, is $T_n=a+(n-1)d$
Which can also be written as $T_n=(a-d)+nd$
On comparing this with the given $n^{th}$ term, we get
$T_n=(a-d)+nd=4n+1$
From this, we get
$a-d=1$ and $d=4$
Therefore, first term, $a=5$ and common difference $d=4$.