Answer to Question #88389 in Algebra for JOSH

Question

0, 3, 8, 15...
Generalize the pattern by finding the nth term.
A)
n2
n
B) 2n - 2
C) n2 - 1
D) n3 - 5

Answer 1

The correct version is C. The sequence numbering starts from 1. For the first element, we need to subtract 1. To get 0, we need to subtract 1. So far, the formula looks like n-1. Substituting the following serial numbers, we can see that the numbers are less than necessary. So you need to increase the number from which we subtract 1. After multiplying n by 2, we get a smaller number. If we raise n to 2 and subtract 1, we get the sequence we need.

0 = n ^ 2-1 (n = 1)

3 = n ^ 2-1 (n = 2)

8 = n ^ 2-1 (n = 3)

15 = n ^ 2-1 (n = 4)