The 6th term on a gp is 2000find it's first term if it's common ratio is 10
To find the first term of the geometric progression (GP), we can use the formula:
\[a_n = a_1 \cdot r^{(n-1)}\]
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
Given that the 6th term (\(a_6\)) is 2000 and the common ratio (\(r\)) is 10, we can substitute these values into the formula:
\[2000 = a_1 \cdot 10^{(6-1)}\]
Simplifying, we get:
\[2000 = a_1 \cdot 10^5\]
Dividing both sides of the equation by \(10^5\):
\[\frac{2000}{10^5} = a_1\]
Simplifying the fraction:
\[0.02 = a_1\]
Therefore, the first term of the geometric progression is 0.02.