The given sequence is 8, 16, 32, ...
To find the equation for this sequence, first observe that each term is a multiple of 8:
- 1st term: \( a_1 = 8 \)
- 2nd term: \( a_2 = 16 = 8 \times 2 \)
- 3rd term: \( a_3 = 32 = 8 \times 4 \)
The next step is identifying the pattern. Notice that each term can also be expressed as:
- \( a_1 = 8 \times 2^0 \)
- \( a_2 = 8 \times 2^1 \)
- \( a_3 = 8 \times 2^2 \)
From this, we can generalize the \( n \)-th term of the sequence as:
\[ a_n = 8 \times 2^{n-1} \]
Thus, the final equation is:
\[ a_n = 8 \times (2)^{n-1} \]