A geometric sequence has an initial term of 81920 and a common ratio of 0.5 . Based off of this information, what would be the sum of the first twelve terms of this geometric sequence?
A) 157900
B) 163800
C) 175400
D) 182500
E) None of the above.

Question

A geometric sequence has an initial term of 81920 and a common ratio of  0.5 . Based off of this information, what would be the sum of the first twelve terms of this geometric sequence?
A) 157900
B) 163800
C) 175400
D) 182500
E) None of the above.

Quizplus · Accepted Answer

The sum of the first n terms of a geometric sequence is given by the formula S_n = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio. For this sequence, a = 81920, r = 0.5, and n = 12. Plugging these values into the formula gives S_12 = 81920(1 - 0.5^12) / (1 - 0.5) = 163840(1 - 0.000244140625) = 163840 * 0.999755859375 = 163800.

A Geometric Sequence Has an Initial Term of 81920 and a Common