Answer (Detailed Solution Below)

Option 3 : 74
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NDA 01/2025: English Subject Test
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Detailed Solution

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Concept:

Let us consider sequence a1, a2, a3 …. an is an A.P.

  • Common difference “d”= a2 – a1 = a3 – a2 = …. = an – an – 1
  • nth term of the A.P. is given by an = a + (n – 1) d

 

Calculation:

Given series is 2, 6, 10, ...,146

First term, a = 2, last term, an = 146, 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.

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