The middle term of arithmatic series 2, 6, 10, ...,1461. 702. 793. 744

1.	The middle term of arithmatic series 2, 6, 10, ...,1461. 702. 793. 744. 83
Answer» Correct Answer - Option 3 : 74 Concept: Let us consider sequence a₁, a₂, a₃ …. a_n is an A.P. Common difference “d”= a₂ – a₁ = a₃ – a₂ = …. = a_n – a_{n – 1} n^th term of the A.P. is given by a_n = a + (n – 1) d Calculation: Given series is 2, 6, 10, ...,146 First term, a = 2, last term, a_n = 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.

The middle term of arithmatic series 2, 6, 10, ...,1461. 702. 793. 744. 83

Answer» Correct Answer - Option 3 : 74

Concept:

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

Common difference “d”= a₂ – a₁ = a₃ – a₂ = …. = a_n – a_{n – 1}

n^th term of the A.P. is given by a_n = a + (n – 1) d

Calculation:

Given series is 2, 6, 10, ...,146

First term, a = 2, last term, a_n = 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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The middle term of arithmatic series 2, 6, 10, ...,1461. 702. 793. 744. 83

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