The first term of a geometric sequence is 8000 and the fifth term is 500. determine the common ratio and the sum of the first nine terms

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:

For, n = 5  

or,

Hence in the given GP, a   = 8000 and r = 1/2

Now, in a  GP sum of n terms is

So, for n = 9,

So,the sum of 9 terms of GP is 15,968.75.

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !