Question

Which of the following is/are the term(s) of an AP whose first term is 2 and the common difference is 4?

• A. 23
• B. 46
• C. 69
• D. 92

Answer 1

The correct option is B

46

Given that $a=2$ and $d=4$
Now, in an AP, $a_n=a+(n-1)d$, where $a_n$ stands for $n^{th}$ term of the AP
Now, $n$ can take values 1,2,3,4……
In other words, $n$ has to be a natural number as $n$ is the position of the term in the AP
Now, $a_n=a+(n-1)d=2+(n-1)4=4n-2$
Verifying options, when $a_n$ = 23,
$a_n=4n-2=23$
$4n=25$
$n=\frac{25}{4}$
Clearly, n is not a natural number
When $a_n=46$
$a_n=4n-2=46$
$4n=48$
n=12, which is a natural number
Similarly, if we verify the remaining options, we see that $n$ is not a natural number when $a_n$ = 69 or 92
Hence, only 46 is a term of the AP.