Which of the following is a term of an AP whose first term is 2 and the common difference is 4?

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Solution

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 $n^{t h}$ 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, $a_{n} = a + (n - 1) d = 2 + (n - 1) 4 = 4 n - 2$
Verifying options, when $a_{n}$ = 23,
$a_{n} = 4 n - 2 = 23$
$4 n = 25$
$n = \frac{25}{4}$
Clearly, n is not a natural number
When $a_{n} = 46$
$a_{n} = 4 n - 2 = 46$
$4 n = 48$
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.

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