Question

In the sequence ,the first term is $4$ and each term after the first is $7$ more than the previous term. What is the ${12}^{th}$ term of the sequence?

• A. $77$
• B. $81$
• C. $84$
• D. $86$
• E. $92$

Answer 1

The correct option is B $81$

Given, first term of the arithmetic progression $\left(AP\right)$ $=$ $4$

Common difference of $AP$ $=$ $7$

We know that

$n^{th}$ term of an $AP$ $=$ $a$ $+$ $(n$ $-$ $1)d$

To find ${12}^{th}$ term of an $AP$,

Here, $a$ $=$ $4$, $d$ $=$ $7$ and $n$ $=$ $12$

${12}^{th}$ term of an $AP$ $=$ $a$ $+$ $(n$ $-$ $1)d$

$=$ $4$ $+$ $(12$ $-$ $1)7$

$=$ $4$ $+$ $(11$ $\times$ $7)$

$=$ $4$ $+$ $77$

$=$ $81$

Therefore, ${12}^{th}$ term of the sequence is ${}^{\prime }{81}^{\prime }$.