SOLUTION: write the rule for the sequence 2, 9, 21, 38,... I was recently given an answer but one of the differences that I was given was wrong Someone gave me 9-21= 11 That would be w

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Question 713629: write the rule for the sequence 2, 9, 21, 38,...
I was recently given an answer but one of the differences that I was given was wrong
Someone gave me 9-21= 11 That would be wrong so would there be a pattern and formula
Answer by kevwill(135) About Me  (Show Source):
You can put this solution on YOUR website!
From the sequence:

2, 9, 21, 38, ...,

the differences between terms are:

7, 12, 17, ...

and the second level differences are:

5, 5, 5, ...

So we know that the first term of the formula is %285%2F2%29%2An%5E2. A little experimentation shows that the actual formula is:

%285%2An%5E2+-+n%29%2F2

So the sequence continues

2, 9, 21, 38, 60, 87, 119, ...