Question

Write an equation to describe the sequence below.Use n to represent the position of a term in the sequence,where n = 1 for the first term.
29,58,116
Write your answer using decimals and integers.
an = __ (__)n-1

Answer 1

To find an equation for the sequence 29, 58, 116, we first look for a pattern.

1. Identify the common ratio or pattern:
- The second term (58) is double the first term (29).
- The third term (116) is double the second term (58).

This suggests that the terms are being multiplied by 2 as we progress through the sequence.

2. The sequence can be viewed as:
- \( a_1 = 29 \)
- \( a_2 = 2 \cdot a_1 = 2 \cdot 29 \)
- \( a_3 = 2 \cdot a_2 = 2 \cdot (2 \cdot 29) \)

Thus, we can express the general term for \( n \) as:
- \( a_n = 29 \cdot 2^{(n-1)} \)

So the equation that describes the sequence is:

\[
a_n = 29(2)^{(n-1)}
\]