Question

find the sum of 51 terms of an A.P whose 2nd term is 2 and 4th term is 8​

Answer 1

Sn = n/2[2a + (n − 1)d]

Where; a = first term for the given A.P.

d = common difference of the given A.P.

n = number of terms 51 terms of an AP

whose a2 = 2 and a4 = 8 We know that, a2 = a + d 2 = a + d …(2)

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, Sn = 512512[2(−1) + (51 − 1)(3)]

= 512512[−2 + 150] = 512512[158] = 3774

Hence, the sum of first 51 terms for the A.P. is 3774