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3 years ago

How many terms are there in a geometric series if the first term is 3, the common ratio is 4 and the sum of the series is 1,023

1 answer:

4 0

The sum of a geometric sequence is:

s(n)=a(1-r^n)/(1-r) in our case:

s(n)=3(1-4^n)/(1-4)

s(n)=-(1-4^n)

s(n)=(4^n)-1 and s=1023

(4^n)-1=1023

4^n=1024

n ln4=ln1024

n=(ln1024)/(ln4)

n=5

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Then you would distribute the $3$ across the parentheses next to it, like this:

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