The general term of a sequence is given a_{n} = 2^{n}. Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference,

foass77W

foass77W

Answered question

2020-11-30

The general term of a sequence is given an=2n. Determine whether the sequence is arithmetic, geometric, or neither.
If the sequence is arithmetic, find the common difference, if it is geometric, find the common ratio.

Answer & Explanation

Aniqa O'Neill

Aniqa O'Neill

Skilled2020-12-01Added 100 answers

If the subsequent terms in a series differ by a constant (common difference), the sequence is an arithmetic sequence (d).
nth term of an an arithmetic sequence an=a+(n1)d


If there is a constant ratio between the terms in a series, the sequence is a geometric sequence.
nth term of an a geometric sequence an=arn

an=2n
Substitute n = 0
a0=20=1
Substitute n=1
a1=21=2
Substitute n=2
a2=22=4
Substitute n=3
a3=23=8

The difference between first and second term is 21=1.
The difference between second and third term is 42=2. since, the successive terms is not differ by a constant. hence the sequence is not an arithmetic sequence.
The ratio of second term to first term is 21=2.
The ratio of third term to second term is 42=2.
The ratio of fourth term to third term is 84=2.
The ratio between successive terms is constant. hence the sequence is a geometric sequence.

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