Question

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

A
23
B
46
C
69
D
92

Solution

## The correct option is B 46Given that a = 2 and d = 4 Now, in an AP, an= a +(n-1)d, where an stands for nth 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,  an=a+(n−1)d=2+(n−1)4=4n−2 Verifying options, when an = 23, an=4n−2=23 4n=25 n=254 Clearly, n is not a natural number When an=46 an=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 an = 69 or 92 Hence, only 46 is a term of the AP.

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