SOLUTION: The first term of geometric progression is 300 and the fourth term is -8/5. Find the common ratio and the sum to infinity.

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Question 1187236: The first term of geometric progression is 300 and the fourth term is -8/5. Find the common ratio and the sum to infinity.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
the first term is a%5B1%5D=300+
the fourth term is a%5B4%5D=-8%2F5
the nth term formula is:
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29
find the common ratio
a%5B4%5D=a%5B1%5D%2Ar%5E%284-1%29=-8%2F5
a%5B4%5D=a%5B1%5D%2Ar%5E3
a%5B4%5D=300%2Ar%5E3
300%2Ar%5E3=-8%2F5
r%5E3=%28-8%2F5%29%2F300
r%5E3=-2%2F375
r=root%283%2C-2%2F375%29
r=root%283%2C-2%2F375%29
a%5Bn%5D=300%2A%28root%283%2C-2%2F375%29%29%5E%28n-1%29

sum%28300%28root%283%2C-2%2F375%29%29%5E%28n-1%29%2Cn=1%2Cinfinity+%29=> converges