Question

analyze the following pattern 1,2,5,10,17..... describe the pattern can someone help me with my apex

Answer 1

Quadratic sequence with

nth term = n^2 - 2n + 2.

Explanation:

1,2,5,10,17

The differences between terms are

1,3,5,7

and the second differences are

2,2,2

This is a quadratic sequence with first term n^2 ( where n = sequence number).

List the original sequence and the values of n^2:-

1 2 5 10 17

1 4 9 16 25

If we subtract the first list from the second we get

0 2 4 6 8 which is arithmetic with common difference 2 and first term 0

The nth term of this is 2(n - 1)

So the explicit formula for the nth term of the original sequence is

n^2 - 2(n - 1)

= n^2 - 2n + 2

Answer 2

First differences start at 1 and increase by 2.

Explanation:

Whenever analyzing any sort of sequence, it is usually helpful to look at the differences between terms. Here, they are ...

... 1, 3, 5, 7

This set of numbers clearly increases by 2 from one to the next. That is, second differences are 2.

_____

When 2nd differences are constant, the pattern can be described by a 2nd-degree polynomial. In this case, that is

... n² -2n +2 . . . . for n = 1, 2, 3, ...