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The GMAT Math practice question given below is a sequences and series question based on summing terms of an Arithmetic Progression

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

1. 300
2. 120
3. 150
4. 170
5. 270

The correct choice is (C) and the correct answer is 150.

The sum of the 4^th and 12^th term = 20.

Let t1 be the first term, t4 be the fourth term, and t12 be the 12^th term

Then t4 + t12 = 20

t4 can be expressed as t1 + 3d
Similarly, t12 can be expressed as t1 + 11d

Then t4 + t12 = 20 can be expressed as   t1 + 3d + t1 + 11d = 20

=>      2t1 + 14d = 20
=>      t1 + 7d =10
=>      t8 = 10

The sum of the first 15 terms =
In an arithmetic progression t1 + t15 = t1 + t1 + 14d = 2t1 + 14d = 2(t1 + 7d) = 2(t8).
Therefore, the sum of the first 15 terms = = 150