Question

From the following options, only can be a term of AP whose first term is 2 and the common difference is 4.

• A. 23
• B. 69
• C. 46
• D. 92

Answer 1

The correct option is C 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.