Question

what is the 9th term in a geometric sequence with a common ratio of 2 and a first term of 3

Answer 1

To find the 9th term in a geometric sequence, you can use the formula for the nth term of a geometric sequence:

\[
a_n = a_1 \cdot r^{(n-1)}
\]

where:
- \( a_n \) is the nth term,
- \( a_1 \) is the first term,
- \( r \) is the common ratio, and
- \( n \) is the term number.

In your case:
- \( a_1 = 3 \)
- \( r = 2 \)
- \( n = 9 \)

Now substitute these values into the formula:

\[
a_9 = 3 \cdot 2^{(9-1)} = 3 \cdot 2^{8}
\]

Now calculate \( 2^{8} \):

\[
2^{8} = 256
\]

Now multiply it by 3:

\[
a_9 = 3 \cdot 256 = 768
\]

Thus, the 9th term in the geometric sequence is **768**.