270,581 views
23 votes
23 votes
Find an explicit formula for the arithmetic sequence -11, -3, 5, 13, ....

Note: the first term should be b(1).
b(n) =

User HelloWorldPeace
by
2.6k points

1 Answer

21 votes
21 votes

Answer:

b(n) = -11 + (n-1)*8

Explanation:

Let n be the sequence number, with n=1 the first number b(1) -11

The sequence changes by +8 each step.

b(1) -11 + 8 = -3

b(2) -3 + 8 = 5

b(3) 5 + 8 = 13

b(4) 13

b(1) = -11

b(2) = -3. or b(1) + 1*8

b(3) = 5, or b(1) + 2*8

b(4) = 13, or b(1) + 3*8

We note that each step adds a multiple of 8 to the initial value of -11. This can be stated as (n-1)*8

The formula for this sequence would be b(n) = b(1) + (n-1)*8

b(n) = -11 + (n-1)*8

Check: Does n=3 return the value of 5?

b(n) = -11 + (n-1)*8

b(3) = -11 + ((3)-1)*8

b(3) = -11 + (2)*8

b(3) = -11 + 16

b(3) = 5 YES