Find the sum of the terms in the geometric sequence.
-54, 18, 6, 2, . . .
A)54
B)81
C)78
D)- 27

Question

Quizplus · Accepted Answer

The given sequence is a geometric sequence where each term is divided by 3 to get the next term. The first term $a = 54$ and the common ratio $r = \frac{1}{3}$. The sum of an infinite geometric sequence is given by $S = \frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. Substituting the given values, we get $S = \frac{54}{1 - \frac{1}{3}} = \frac{54}{\frac{2}{3}} = 54 \times \frac{3}{2} = 81$.

Find the Sum of the Terms in the Geometric Sequence