SOLUTION: The following problem refers to a geometric sequence: Given a_9=781250 and a_12=97656250, find r

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Question 1161322: The following problem refers to a geometric sequence:
Given a_9=781250 and a_12=97656250, find r
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:

a%5B9%5D=781250
a%5B12%5D=97656250
find+r

use nth term formula:
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29
substitute a%5B9%5D=781250

781250=a%5B1%5D%2Ar%5E%289-1%29

781250=a%5B1%5D%2Ar%5E8..........solve for a%5B1%5D

a%5B1%5D=781250%2Fr%5E8....eq.1

substitute a%5B12%5D=97656250

97656250=a%5B1%5D%2Ar%5E%2812-1%29

97656250=a%5B1%5D%2Ar%5E11..........solve for a%5B1%5D

a%5B1%5D=97656250%2Fr%5E11....eq.2

from eq.1 and eq.2 we have

781250%2Fr%5E8=97656250%2Fr%5E11

781250r%5E11%2Fr%5E8=97656250

781250r%5E%2811-8%29=97656250

781250r%5E3=97656250

r%5E3=97656250%2F781250

r%5E3=125

highlight%28r=5%29

go to

a%5B1%5D=781250%2Fr%5E8....eq.1, substitute r

a%5B1%5D=781250%2F5%5E8

a%5B1%5D=781250%2F390625

a%5B1%5D=2

and nth term formula is:

a%5Bn%5D=2%2A5%5E%28n-1%29