The given sequence is: 10, 20, 40, ...
To find an equation for this sequence, we first observe the pattern.
- The first term (n = 1): \( a_1 = 10 \)
- The second term (n = 2): \( a_2 = 20 \)
- The third term (n = 3): \( a_3 = 40 \)
We can see that each term in the sequence is double the previous term. More explicitly:
- \( a_2 = 2 \times a_1 = 2 \times 10 = 20 \)
- \( a_3 = 2 \times a_2 = 2 \times 20 = 40 \)
Therefore, it appears that the sequence can be described by the recurrence relation:
- \( a_n = 2 \times a_{n-1} \)
If we want to express \( a_n \) directly in terms of \( n \), we can see that:
- The \( n \)-th term can be written in terms of powers of 2:
\[ a_n = 10 \times 2^{n-1} \]
Thus, the equation to describe the sequence is:
\[ a_n = 10 \times 2^{n - 1} \]