Find the 9th term of the geometric sequence 4, - 16, 64
To find the 9th term of a geometric sequence, we use the formula:
\[ a_n = a_1 \times r^{n-1} \]
where:
- \( a_n \) is the n-th term
- \( a_1 \) is the first term
- \( r \) is the common ratio
- \( n \) is the term number
Given the sequence 4, -16, 64, we can see that:
- \( a_1 = 4 \)
- \( r = -4 \) (to get from 4 to -16, we multiply by -4; to get from -16 to 64, we also multiply by -4)
Now, we want to find the 9th term, so we substitute these values into the formula:
\[ a_9 = 4 \times (-4)^{9-1} \]
\[ a_9 = 4 \times (-4)^8 \]
\[ a_9 = 4 \times 65,536 \]
\[ a_9 = 262,144 \]
Therefore, the 9th term of the geometric sequence 4, -16, 64 is 262,144.