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

Question

Mathematics

Kyra

15 April, 18:52

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

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Answers (1)

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Layla Craig · Answer 1

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