Question

For a G.P. if a = 5 and $\rm t_{7} =\frac{1}{3125}$, find r and $\rm t_{9}$.

Answer 1

Answer:

Step-by-step explanation:

The general form of G.P is

$a, ar, ar^2, ar^3,.........$

It's n th term is

$t_{n}=ar^{n-1}$

Given:

a=5

$t_{7}=\frac{1}{3125}\\\\ar^{6}=\frac{1}{3125}\\\\(5)r^{6}=\frac{1}{3125}\\\\r^{6}=\frac{1}{5(3125)}\\\\r^{6}=\frac{1}{5^6}\\\\r^{6}=(\frac{1}{5})^6\\\\r=\frac{1}{5}$

$t_{n}=ar^{n-1}\\\\t_{9}=ar^{8}\\\\t_{9}=(5)(\frac{1}{5})^{8}\\\\t_{9}=(5)\frac{1}{5^8}\\\\t_{9}=\frac{1}{5^7}\\\\t_{9}=\frac{1}{15625}$