Answer:
The common ratio = 1/2
The sum of 9 terms of GP is 15,968.75
Step-by-step explanation:
Here, in the given GP:
Firs Term a = 8000, Fifth term a(5) = 500
Let Common Ratio = r
Now, by the general term of GP:
[tex]a_n = a \times (r)^{n-1}[/tex]
For, n = 5 [tex]a_5 = a \times (r)^{5-1}[/tex]
or, [tex]500 = 8000 \times (r)^{4}\\\implies (r)^{4} = \frac{500}{8000} = \frac{1}{16} = \frac{1}{(2)^4} \\\implies r= \frac{1}{2}[/tex]
Hence in the given GP, a = 8000 and r = 1/2
Now, in a GP sum of n terms is [tex]s_n = \frac{a(1-r^n)}{1-r}[/tex]
So, for n = 9, [tex]s_9 = \frac{8000(1- (\frac{1}{2}) ^9)}{1-\frac{1}{2} } = \frac{8000(1- 0.001953)}{0.5 }\\= \frac{8000 \times (0.9980)}{0.5} = 15,968.75[/tex]
So,the sum of 9 terms of GP is 15,968.75.
