Write the explicit formula for the apparent Nth term

Question

Write the explicit explicit formula for the apparent Nth term

0,3,8,15,24,

Answer 1

0, 3, 8, 15, 24, 35, 48, ... (notice that each term is 1 less than a perfect square)

1----->0

2----->3

3----->8

4----->15

5----->24

6----->35

7----->48

etc....

this should help you to see the relationship between the term number and the term

1^2-1=0

2^2-1=3

3^2-1=8

4^2-1=15

5^2-1=24

6^2-1=35

7^2-1=48

etc...

A(n)=n^2-1 is the explicit formula

Answer 2

The difference between two terms in the next odd #

3-0 = 3

8-3 = 5

15 - 8 = 7

24 - 15 = 9

35 - 24 = 11

so the sequence is 0,3,8,15,24,35,48,63,80,99,120,....

The recursive formula is

A_n = A_(n-1) + (2*n-1) where A1=0 and n=2,3,4,.....

The explicit formula is: N^2-1 for n=1,2,3,4,5,

Answer 3

The sequence 0, 3, 8, 15, 24, ...

is not an arithmetic sequence -- there is not a common difference between adjacent terms.

is not a geometric sequence -- there is not a common ratio between adjacent terms.

We now look for a pattern:

The value of each term is larger.

The difference between terms gets larger and larger.

The difference of 3, 5, 7, and 9 reveals a pattern.

[note that the sequence n² is 1, 4, 9, 16, 25, ... and (n² - 1) is 0, 3, 8, 15, 24. ...]

You may write the sequence using the explicit formula:

a_n = n² - 1 for n>0

Note that a term in the explicit formula depends only on the value of n, not on the value of any of the other terms.