The 6th term of a gp 2000. Find its first term if its common ratio is 10
No
0.02.02 2 20 200 2000
To find the first term of a geometric progression (GP), we can use the formula:
\[a_n = a_1 \cdot r^{(n-1)}\]
where \(a_n\) is the \(n\)th term of the GP, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the position of the term in the GP.
In this case, we are given that the 6th term of the GP is 2000 and the common ratio is 10. So we have:
\[a_6 = a_1 \cdot 10^{(6-1)} = 2000\]
Simplifying the equation:
\[a_1 \cdot 10^5 = 2000\]
Divide both sides of the equation by \(10^5\):
\[a_1 = \frac{2000}{10^5}\]
Calculating the right side of the equation:
\[a_1 = \frac{2000}{100000} = \frac{1}{50}\]
Therefore, the first term of the geometric progression is \(1/50\).
so ar^5 = 2000, and you told me r = 10
a(10^5) = 2000
a = 2000/100000 = 1/50