SOLUTION: Write an expression for the apparent nth term of the sequence, assume that n begins with 1: -1,2,7,14,23... We know that we are to figure out the relationship between n and the

Question 971762: Write an expression for the apparent nth term of the sequence, assume that n begins with 1:
-1,2,7,14,23...
We know that we are to figure out the relationship between n and the terms, but I just can't seem to figure it out.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Your dash sign at the start must be an accidental stray character. There is a difference pattern showing.

1 to 2, added 1.
2 to 7, added 5.
7 to 14, added7...........

Now the dash must really be intentional.
-1 to 2, added 3.
2 to 7, added 5.
7 to 14, added 7.
14 to 23, added 9.

-1 to 2, added 3._______-1+2+1, n=2
2 to 7, added 5._______-1+(2+1)+(2+3), n=3
7 to 14, added 7.______-1+(2+1)+(2+3)+(2+5), n=4
14 to 23, added 9._____-1+(2+1)+(2+3)+(2+5)+(2+7), n=5

Each term is based on a summation.
You may be able to finish this on your own. You will need to think carefully about each section shown above.

(2+1+(n-2)2),
(2+(1+(n-2)*2)), represents the last expression added.
Does this work for n=3? n=5?
Yes for n=3; yes for n=5.

NOTE: The above shown work is a search for the pattern. I DID NOT finish answering; I show there the effort of searching for the pattern. Can YOU finish this?
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