Question

Is $51$ a term of the AP, $5,8,11,14,........?$

• A. Yes
• B. No
• C. Ambiguous
• D. Data insufficient
  

Answer 1

The correct option is B No

Given series is $5,8,11,14,....$

Let $51$ be the $n^{th}$ term.

$\therefore a_n=51$
$a=5,d=3$

We know, $a_n=a+(n-1)d$
$\therefore 51=a+(n-1)d$
$51=5+(n-1)3$

$\frac{46}{3}=n-1$

$\frac{46+3}{3}=n$

$n=\frac{49}{3}$
Since $n$ is not a natural no.
$51$ is not a term of AP.