SOLUTION: What is the general term of the arithmetic sequence: -1,-1/4,-1/9,-1/16.......

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Question 1087239: What is the general term of the arithmetic sequence: -1,-1/4,-1/9,-1/16.......
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

-1,-1%2F4,-1%2F9,-1%2F16,.......
look for pattern:

a%5B1%5D=-1
a%5B2%5D=+-1%281%2F4%29=-1%281%2F2%5E2%29
a%5B3%5D=+-1%281%2F9%29=-1%281%2F3%5E2%29
a%5B4%5D=+-1%281%2F16%29=-1%281%2F4%5E2%29
and for nth term will be:
a%5Bn%5D+=+-1%2Fn%5E2 or a%5Bn%5D+=+-1%281%2Fn%5E2%29where n=0,1, 2...
by definition:
Sequences of numbers that follow a pattern of adding a fixed number from one term to the next are called arithmetic sequences.
The d-value can be calculated by subtracting any two consecutive terms in an arithmetic sequence.
d+=+a%5Bn%5D+-+a%5Bn+-+1%5D where n is any positive integer greater than 1
Sequences of numbers that follow a pattern of multiplying a fixed number,called the common ratio, from one term to the next are called geometric sequences.
+a%5Bn%5D+=+r%5Bn%5D%2A+a%5Bn+-+1%5D
so, in your case we have geometric sequence because we multiplying fixed number -1 by the common ratio %281%2Fn%5E2%29