Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.

Question

–1 , –4 , –16 , ...

Write your answer using decimals and integers.

an =
(
)n - 1

Answer 1

To find an equation that describes the sequence \(-1, -4, -16, \ldots\), we need to analyze the pattern of the terms.

The sequence appears to be decreasing, and the terms suggest they can be expressed as powers of \(2\):

1. The first term \(a_1 = -1 = -2^0\)
2. The second term \(a_2 = -4 = -2^2\)
3. The third term \(a_3 = -16 = -2^4\)

From this, we can see that the position \(n\) corresponds to the exponent being \(2(n - 1)\).

Putting this together, we can form the equation representing the \(n\)th term of the sequence:

\[ a_n = -2^{2(n - 1)} \]

So, the equation describing the sequence is:

\[ a_n = -2^{2(n - 1)} \]