SOLUTION: Give an equation for the sequence: =1/2, -1/5, 1/10, -1/17, 1/26, -1/37

Question 375346: Give an equation for the sequence:
=1/2, -1/5, 1/10, -1/17, 1/26, -1/37

Answer by EdwinMcCravy(4) (Show Source): You can put this solution on YOUR website!

The sequence of denominators is 

2, 5, 10, 17, 26, 37, ...

and we notice that each term of this sequence is 1 more than the
corresponding term in the sequence of squares:

1, 4, 9, 16, 25, 36, ...

And we know that the formula for the nth term of that sequence is



So the formula for the nth term of the sequence of denominators 

2, 5 10 17, 26, 37, ...

is 

Then the formula for the nth term of the sequence of the absolute values 
of the terms of the given sequence,

1/2, 1/5, 1/10, 1/17, 1/26, 1/37

is



But the signs alternate in the given sequence.  To cause the signs to alternate,
multiply by the "alternating-sign factor" 

So the final answer is



Edwin

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