Question

write an explicit formula for ( a_n ), the ( n^{\text{th}} ) term of the sequence ( 8, -40, 200, dots ).
answer
attempt 1 out of 2
( a_n = ) input box submit answer

Explanation:

Step1: Identify the sequence type

The sequence is \(8, -40, 200, \dots\). Check if it's geometric by finding the common ratio \(r\).
\(r=\frac{-40}{8}=-5\), \(\frac{200}{-40}=-5\), so it's a geometric sequence.

Step2: Recall geometric sequence formula

The explicit formula for a geometric sequence is \(a_n = a_1 \cdot r^{n - 1}\), where \(a_1\) is the first term and \(r\) is the common ratio.

Step3: Substitute values

Here, \(a_1 = 8\) and \(r=-5\). Substitute into the formula:
\(a_n = 8 \cdot (-5)^{n - 1}\)

Answer:

\(8 \cdot (-5)^{n - 1}\)