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Question

The sum of the fourth and twelfth terms of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

A
150
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B
200
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C
250
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D
500
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Solution

The correct option is A 150
Given a4+a12=20
To Find Sum of the first 15 terms.

Expression for nth term of an A.P whose first term is a and common difference is d is given by an=a+(n1)d.
a4+a12=20
a+3d+a+11d=20
2a+14d=20

Expression for sum of first n terms of an A.P whose first term is a and common difference is d is given by Sn=n2[2a+(n1)d].
S15=152(2a+14d)=15×202=150

So, the sum of the first 15 terms of the A.P is equal to 150.

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