1. Analyze the following pattern: 1, 2, 5, 10, 17,

n² - 2n + 2

Step-by-step explanation:

The difference in the pattern are odd numbers.

2 - 1 = 1

5 - 2 = 3

10 - 5 = 5

17 - 10 = 7

So there is a - 2n in the nth term.

If we subtract 1 on each term.

0, 1, 4, 9, 16

We get whole squares.

So there is a n² in the nth term.

(1) ² - 2 (1) + c = 1

1 - 2 + c = 1

-1 + c = 1

c = 2

The nth term is:

n²-2n+2