How to find General term for 1,0,3,10,21,36,55.....?

Question

How to find General term for 1,0,3,10,21,36,55.....?

Answer 1

1 = (-1) * (-1)

0 = 0 * 1

3 = 1 * 3

10 = 2 * 5

21 = 3 * 7

36 = 4 * 9

55 = 5 * 11

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answer : T(n) = (n - 2)[2(n - 2) + 1] = (n - 2)(2n - 3)

Answer 2

Every number is added by a number plus 4.  

n = number (starting at 0)

a = adding number (starting at 3)

n = (n + (a + 4))

Answer 3

look at the difference between each successive term and the one preceding.

0 - 1 = -1

3 - 0 = 3

10 - 3 = 7

21 - 10 = 11

Do you see any pattern ?  What should the next difference be ?  Is that what it is ?

Can you figure out the pattern now ?  Look in your book for the notation to use in writing the general term...

Good luck.