GMAT MATH - Arithmetic Progression

June 09, 2004

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?

(A)	300
(B)	120
(C)	150
(D)	170
(E)	270

Correct Choice (C) Answer (150)

Explanatory Answer

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

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

Then t4 + t12 = 20
ð     t1 + 3d + t1 + 11d = 20
ð     2t1 + 14d = 20
ð     t1 + 7d =120
ð     t8 = 10.

The sum of the first 15 terms =
In an arithmetic progression t1 + t15 = t2 + t14 = t3 + 13 =... = t8 + t8.
Therefore, the sum of the first 15 terms == 150