Write the first five terms of the geometric sequence with a = 5 and a fourth term of 135.
A) 5, 15, 45, 135, 405
B) 5, 16, 41, 138, 405
C) 5, 15, 46, 138, 402
D) 5, 8, 11, 14, 17

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 $a_1$ is the first term, $a_n$ is the nth term, and $r$ is the common ratio. Given $a_1 = 5$ and the fourth term $a_4 = 135$, we can solve for $r$: $135 = 5 \cdot r^{(4-1)}$, which simplifies to $135 = 5 \cdot r^3$. Solving for $r$, we find $r = 3$. Thus, the first five terms, starting with 5 and multiplying each successive term by 3, are 5, 15, 45, 135, 405.

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