An AP consists of 23 terms. If the sum of the three terms in the middle is 141 and the sum of the last three terms is 261, then the first term is

An AP consists of 23 terms. If the sum of the three terms in the middle is 141 and the sum of the last three terms is 261, then the first term is

(1) 6

(2) 5

(3) 4

(4) 3

Solution:

Let a1,a2,…a23 be the terms in AP.

Let d be the common difference.

Given a11+a12+a13 = 141

a+10d+a+11d+a+12d = 141

3a+33d = 141

a+11d = 47 ..(i)

Sum of last 3 terms=> a+20d+a+21d+a+22d = 261

3a+63d = 261

a+21d = 87 ..(ii)

Solving (i) and (ii), we get d = 4

Substitute d in (i), we get

a+44 = 47

a = 3

Hence option (4) is the answer.

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