A pattern rule for a sequence

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Question from Grace, a parent:

Here's a Grade 7 question, we need to find the pattern rule:

1 - 1
2 - 3
3 - 6
4 - 10
......
It may involve exponents, but we can't seem to figure it out.
thank you.
Grace.

Hi Grace,

One of the techniques to try is to look at successive differences. Suppose the sequence is

1 - 3
2 - 5
3 - 9
4 - 17
.....
Here the successive differences are

5 - 3 = 2
9 - 5 = 4
17 - 9 = 8

so the differences are powers of two, $2^1=2, 2^2 = 4, 2^3 = 8$ and so on.

Try this with your sequence and write back if you need more assistance
Penny

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