A geometric sequence is defined recursively by a_n=4a_(n−1), and the first term of the sequence is 0.5, how do you find the explicit formula?

Winston Todd

Winston Todd

Answered question

2022-10-25

A geometric sequence is defined recursively by a n = 4 a n - 1 , and the first term of the sequence is 0.5, how do you find the explicit formula?

Answer & Explanation

exalantaswo

exalantaswo

Beginner2022-10-26Added 14 answers

Looking at this we have...
a n = 4 a n - 1

a 2 = 4 a 2 - 1
a 2 = 4 a 1
a 2 = 4 0.5
a 2 = 2

Since we are told that is a geometric sequence there has to be a r or a common ratio:
r = a 2 a 1
r = 2 5 = 4

So explicitly written, the formula would be:
a n = 0.5 ( 4 ) n - 1

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