Question

write explicit formula for sequence
question
write an explicit formula for $a_n$, the $n^{\text{th}}$ term of the sequence
$3, -18, 108, \dots$
answer
attempt 1 out of 2
$a_n = $

Explanation:

Step1: Identify sequence type

This is a geometric sequence, where each term is multiplied by a common ratio $r$ to get the next term.

Step2: Calculate common ratio $r$

$r = \frac{-18}{3} = -6$, or $\frac{108}{-18} = -6$

Step3: Use geometric sequence formula

The explicit formula for a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, where $a_1=3$ is the first term.
Substitute values:
$a_n = 3 \cdot (-6)^{n-1}$

Answer:

$a_n = 3 \cdot (-6)^{n-1}$