Find an explicit formula for the arithmetic sequence -5,13,31,49...

b(n)=__

Given:

Arithmetic sequence    -5, 13, 31, 49

We are to find the explicit formula of the sequence above. An explicit formula provides a binding formula for finding nth term.

To find the formula, we need to know the  first term and the common difference.

The common difference is the difference between each successive terms of the sequence.

In the given sequence, the common difference is 18;

      13-(-5) = 18

      31 - 13 = 18

      49 - 31 = 18

n    calculation of the nth term

1              -5                          -5  +  18(0)  = -5

2             13                          -5   + 18(1)  = 13

3             31                          -5   +  18(2)  = 31

4             49                         -5   +  18(3)  = 49

Since the common difference is 18, we can now derive the formula;

          b(n) = -5 + 18(n-1)

n is the position of the term

Any number in the sequence can be derived using the explicit formula

-5 + 18(n-1)

no pictures of the graph

sine

step-by-step explanation: