Arithmetic Sequence to Linear Function

We will start with the explicit formula. Given the following sequence, state the first term and common difference. Example 1:          4, 7, 10, 13, 16, …

Now, write the explicit formula for the given sequence.

Example 1:          4, 7, 10, 13, 16, …

Write an explicit rule to model the following sequence: Example 2: 21, 19, 17, 15, …

Write and explicit rule to model the following sequence:

Write a function to represent the sequence:
 -12, -11.75, -11.5, -11.25…?

• f(n) = 0.25n - 12

• f(n) = -0.25(n - 1) - 12

• f(n) = 0.25n - 12.25

• f(n) = 12(n -1) - 0.25

Linear Functions relate to the:

• A. Geometric Sequence

• B. Arithmetic Sequence

• C. Exponential Sequence

The "b" value in f(x)=mx+b for arithmetic sequences represents what?

• first term

• term we're looking for, minus one

• common difference

• common ratio

Now, let's go backwards!!! Given the explicit formula, list the first five terms in order. (You can ignore term 0)

• 2, 5, 8, 11, 14, ...

• 3, 1, -1, -3, -5, ...

• 3, 6, 9, 12, 15, ...

• 3, 5, 7, 9, 11, ...

Create the explicit formula for the sequence: 2, 8, 14, ...

(Hint: Use the common difference AND the zero term!.)

• a_n = 6n + 2

• a_n = 6n - 6

• a_n = 6n - 4

• a_n = -6n + 4

Find the 25th term of the sequence if a₁ = 5 and d = 0.5

• 18

• 17

• 15

• 14