Find the 10th term of a Gp whose 8th term is 768and the common ratio is 2
To find the 10th term of the geometric progression (GP), we need to use the formula for the nth term of a GP:
\[a_n = a_1 \times r^{(n-1)}\]
where:
- \(a_n\) is the nth term of the GP
- \(a_1\) is the first term of the GP
- \(r\) is the common ratio of the GP
- \(n\) is the term number we want to find
Given that the 8th term (\(a_8\)) is 768 and the common ratio (\(r\)) is 2, we can set up the equation:
\[768 = a_1 \times 2^{(8-1)}\]
Simplifying:
\[768 = a_1 \times 2^7\]
\[768 = a_1 \times 128\]
Dividing both sides by 128:
\[\frac{768}{128} = a_1\]
\[6 = a_1\]
Now we can find the 10th term (\(a_{10}\)) using the formula:
\[a_{10} = a_1 \times 2^{(10-1)}\]
\[a_{10} = 6 \times 2^9\]
\[a_{10} = 6 \times 512\]
\[a_{10} = 3072\]
Therefore, the 10th term of the geometric progression is 3072.