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Question

An AP consists of 23terms. If the sum of the three terms in the middle is 141. and the sum of the last three terms is261, then the first term is


A

6

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B

5

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C

4

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D

3

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Solution

The correct option is D

3


The explanation for the correct option:

Step 1. Assume the variables :

Let a1,a2.........,a23be the terms in AP.

Let dbe the common difference.

Step 2. Apply the given condition :

the sum of the three terms in the middle is 141.

a11+a12+a13=141a+10d+a+11d+a+12d=141[an=a+(n-1)d]3a+33d=141a+11d=47..............(1)

the sum of the last three terms is 261.

a21+a22+a23=261a+20d+a+21d+a+22d=2613a+63d=261a+21d=87.............(2)

Step3. Solving the equation :

Solving (1) and (2), we get d=4

Substitute din (1), we get

a+44=47a=3

Thus, the first term is 3.

Hence, the correct option is D.


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