foass77W
2020-11-30
The general term of a sequence is given
If the sequence is arithmetic, find the common difference, if it is geometric, find the common ratio.
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
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
Substitute n = 0
Substitute n=1
Substitute n=2
Substitute n=3
The difference between first and second term is .
The difference between second and third term is . 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
The ratio of third term to second term is .
The ratio of fourth term to third term is
The ratio between successive terms is constant. hence the sequence is a geometric sequence.
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