Find an explicit rule for the nth term of the sequence.
-The second and fifth terms of a geometric sequence are $- 16$ and 128 , respectively.
A) $a _ { n } = 8 \cdot ( - 2 ) ^ { n + 1 }$
B) $a _ { n } = 8 \cdot 2 ^ { n }$
C) $a _ { n } = 8 \cdot ( - 2 ) ^ { n - 1 }$
D) $a _ { n } = 8 \cdot 2 ^ { n - 1 }$

Question

Quizplus · Accepted Answer

The sequence is geometric, so the ratio between consecutive terms is constant. Given the second term is $-16$ and the fifth term is $128$, we can find the common ratio $r$ by noting that $128 = -16 \cdot r^3$. Solving for $r$, we get $r = -2$. The first term $a_1$ can be found by dividing the second term by the common ratio: $a_1 = \frac{-16}{-2} = 8$. Thus, the nth term is $a_n = 8 \cdot (-2)^{n-1}$.

Find an Explicit Rule for the Nth Term of the Sequence