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Question

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


Your Answer
A
23
Correct Answer
B
46
Your Answer
C
69
Your Answer
D
92

Solution

The correct option is B 46
Given 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+(n1)d=2+(n1)4=4n2
Verifying options, when an = 23,
an=4n2=23
4n=25
n=254
Clearly, n is not a natural number
When an=46
an=4n2=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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