UPSC NDA Math Model Paper 5

Given series is 2, 6, 10, ...,146
First term, a = 2, last term, an=14 6, an
Common difference d = 4, so it is an AP
an=a+(n–1)d
146 = 2 + (n - 1) (4)
⇒ n - 1 = 144/4
⇒ n = 36 + 1 = 37
So, number of terms in given series = 37
Middle term = (37 + 1)/2 = 19th term
a19=2+(19−1)×4
= 2 + 72
= 74
Hence, option (3) is correct.