Question

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

Answer 1

Step-by-step explanation:

We know that the sum of terms for different arithmetic progressions is given by

Sn = n2n2[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.

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