To find an equation for the sequence 29, 58, 116, we first look for a pattern.
- 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.
- 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:
\[ a_n = 29(2)^{(n-1)} \]