Need to find the explicit formula for the following sequence 1/2,3/4,5/8,7/16 ...

bamakhosimz

bamakhosimz

Answered question

2022-09-07

Need to find the explicit formula for the following sequence 1/2,3/4,5/8,7/16 ...

Answer & Explanation

Jovany Newman

Jovany Newman

Beginner2022-09-08Added 10 answers

The numerators form an arithmetic sequence:
1,3,5,7
with common difference 2.
So a formula for the numerator could be written:
p n = 1 + 2 ( n - 1 ) = 2 n - 1
The denominators form a geometric sequence:
2,4,8,16
with common ratio 2.
So a formula for the denominator could be written:
q n = 2 2 n - 1 = 2 n
Thus a formula for a general term of our example sequence can be written:
a n = p n q n = 2 n - 1 2 n

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