Download 4-7 Arithmetic Sequences Sequence

4-7
Arithmetic Sequences
Sequence: is an ordered list of
numbers that often form a
pattern
Term of a Sequence: What
each number in the list is
called
Arithmetic Sequence: The
difference between consecutive
terms is constant
This difference is called the
Common Difference
Problem 1 and 2: Extending Sequences
and Identifying Arithmetic Sequences
Tell whether the sequence is
arithmetic. If it is find the common
difference and find the next three
terms.
3, 8, 13, 18, …
Tell whether the sequence is
arithmetic. If it is find the common
difference and find the next three
terms.
6, 9, 13, 17
Tell whether the sequence is
arithmetic. If it is find the common
difference and find the next three
terms.
8, 15, 22, 30
Tell whether the sequence is
arithmetic. If it is find the common
difference and find the next three
terms.
10, 4, –2, –8
Problem 3: Writing a Recursive Formula
Formula
𝐴 𝑛
= 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑡𝑒𝑟𝑚 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑒𝑞𝑢𝑒𝑛𝑐𝑒
𝐴 𝑛
= 𝐴 𝑛 − 1 + 𝑐𝑜𝑚𝑚𝑜𝑛 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒
Write a recursive formula for the
arithmetic sequence
70, 77, 84, 91, …
Write a recursive formula for the
arithmetic sequence
97, 88, 79, 70, …
Problem 4: Writing an Explicit Formula
Formula
𝐴 𝑛 =𝐴 1 + 𝑛−1 𝑑
1st
The term of
the sequence
The common
difference of the
sequence
Write an explicit formula for the
arithmetic sequence
3, 7, 11, 15, …
Write an explicit formula for the
arithmetic sequence
3, −2, −7, −12, …