Find nth term rule for 1/2,1/4,1/8,1/16,...

Payton Rasmussen

Payton Rasmussen

Answered question

2022-09-06

Find nth term rule for 1 2 , 1 4 , 1 8 , 1 16 , ...

Answer & Explanation

Kaleb Harrell

Kaleb Harrell

Beginner2022-09-07Added 14 answers

The series 1 2 , 1 4 , 1 8 , 1 16 , ... . can be written as
1 2 1 , 1 2 2 , 1 2 3 , 1 2 4 , ... .
Hence n t h term can be written as 1 2 n .
Other way could be to treat it as a geometric series whose first term is a 1 and common ratio is r. The n t h term of the series is then given by a 1 × r n - 1 .
As here a 1 = 1 2 and r = 1 4 1 2 = 1 4 × 2 1 = 1 2 , the n t h term is
1 2 × ( 1 2 ) n - 1 or
1 2 × 1 2 n - 1 = 1 2 n

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