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Name:
Standard: I can recognize that arithmetic and geometric sequences are functions, sometimes
defined recursively, whose domain is a subset of the integers.
Sequences are a special kind of function. The domain consists of the counting numbers (1,2,3,…).
Sequences can be expressed in two ways, recursively and explicitly. You will practice each below
using the function notation that you have learned.
For each of the following arithmetic sequences, find the common difference (d) and then use
that information to write both an explicit and a recursive function for the sequence.
2.
-10, -4, 2, 8, 14, …
a. d =
b. Recursive Formula fn =
c. Explicit Formula: f(n) =
d. f(7) =
E. f(20) =
3.
10, 8, 6, 4, …
a. d =
b. Recursive Formula fn =
c. Explicit Formula: f(n) =
d. f(7) =
E. f(20) =
4.
36, 31, 26, 21, …
a. d =
b. Recursive Formula fn =
c. Explicit Formula: f(n) =
d. f(7) =
E. f(20) =
Find the number of terms in the following arithmetic sequences. Hint: You will need to find the
explicit formula first and then solve an algebra equation, knowing the final value of the function.
Do NOT write out the entire sequence!
5.
2, 5, 8, …, 299
6.
9, 5, 1, …, -251
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