Write the first four terms of the geometric sequence with a = 12 and a third term of 108.
A) 12, 36, 108, 324
B) 13, 41, 109, 324
C) 12, 37, 109, 323
D) 7, 10, 13, 16

Question

Quizplus · Accepted Answer

The common ratio (r) can be found using the formula for the nth term of a geometric sequence, $a_n = a_1 \cdot r^{(n-1)}$, where $a_n$ is the nth term, $a_1$ is the first term, and $r$ is the common ratio. Given $a_1 = 12$ and the third term $a_3 = 108$, we can solve for $r$: $108 = 12 \cdot r^{(3-1)}$, which simplifies to $108 = 12 \cdot r^2$. Solving for $r$, we get $r = 3$. Thus, the first four terms are $12, 12 \cdot 3 = 36, 36 \cdot 3 = 108$, and $108 \cdot 3 = 324$.

Write the First Four Terms of the Geometric Sequence with a =