How do you find nth term rule for #1/2,1/4,1/8,1/16,...#?

1 Answer
Shwetank Mauria
Aug 21, 2016

#n^(th)# term is #1/2^n#.

Explanation:

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^(th)# 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^(th)# 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^(th)# term is

#1/2×(1/2)^(n-1)# or

#1/2×1/2^(n-1)=1/2^n#.

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