Question

The sum of the first 51 terms of the arithmetic progression 2^nd term is 2 and 4^th term is 8, is _____
1. 3774
2. 7458
3. 3477
4. 7548

Answer 1

Correct Answer - Option 1 : 3774

Given: Given 51 terms of an A.P whose a2 = 2 and  a4 = 8

Concept:

Sum of n terms in A.P is S = (n/2) × [2a + (n − 1) × d]                ---(A)

Calculation:

We know that a₂ = a + d        ---(1)

Also , a₄ = a + 3d

⇒ 8 = a + 3d      ---(2)

Subtracting (1) from (2), we have

⇒ 2d = 6 

⇒ d = 3

Substituting d = 3 in (1), we get 

⇒ 2 = a + 3 

⇒ a = -1

Given that the number of terms (n) = 51 

First term a = -1

So, from equation (A)

S_n = (51/2) × [2(-1) + (51 - 1)(3)]

⇒ (51/2) × [-2 + 150]

⇒ (51/2) × [148]

⇒ 3774