help me pleaseee

Question

Consider the sequence below:

-9, -6, -1, 6, 15 …

What explicit expression can be used to find the nth term of this sequence?

Answer 1

The difference between two terms is 3, then 5, then 7, 9, etc. So they are a sequence of odd numbers. The sum of the k first odd numbers is k² but here we start with 3, and the first term needs to be -9. There's always a tiny of of trial-and-error to adjust for the exact conditions :-) This works:

u(n) = (n + 1)² - 10

Answer 2

The difference between each number is increasing by 2 between each number.

Starting with -9 for n = 0

for n = 1, difference is 3

for n = 2, difference is 5

for n = 3, difference is 7

for n = 4, difference is 9

so difference is 2*n + 1

so starting at n = 1

a(n) = a(n-1) + 2*n + 1