Chapter 9-3 Arithmetic Sequences and Series (Day 1)
Obj: To find the indicated terms of an arithmetic sequence.
Who uses this? – You can use arithmetic sequences to predict costs.
Arithmetic Sequence – is a sequence in which each term after the first is found by adding
a constant, called the common difference “d” to the previous term. [Recall that we just
learned that when writing rules for sequences, linear patterns (and functions for that
matter!) have a constant first difference.]
Terms
1,
5,
+4
9,
+4
13,
+4
17,
+4
21,
+4
25,
+4
29,…
+4
Common Difference (d)
Identifying Arithmetic Sequences:
Determine whether each sequence could be arithmetic. If so, find the
common difference and the next three terms.
a) 91, 83, 75, 67, ____, ____, ____
d = _______
b) -3, 2, 7, 12, 17, ____, ____, ____
d = _______
c) -4, -12, -24, -40, -60, ____, ____, ____
d = ______
What if we want to find the 10th term of an arithmetic sequence? The
50th term? The 99th term? Or…the 𝑛𝑡ℎ term???
General Rule for Arithmetic Sequence – Formula for the 𝑛𝑡ℎ term.
𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑
𝑛𝑡ℎ Term
1st Term
# of Term
Common Difference
Ex 1. Find the 10th term of the following arithmetic sequences:
a) 12, 16, 20, 24,…
b) 32, 25, 18, 11, 4,…
Ex 2. Find the nth term of each arithmetic sequence:
a) 𝑎1 = 3, 𝑑 = −5, 𝑛 = 24
b) 𝑎1 = 14, 𝑑 = 7, 𝑛 = 13
Finding Missing Terms in the arithmetic sequence:
11, ___, ___, ___, -17
1st - Find the common difference
𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑
2nd – sub in -17 for 𝑎𝑛, 11 for 𝑎1,
and 5 for n. Solve for d
Use:
3rd – use d to fill in blanks
You try…Find the missing terms in the arithmetic sequence:
17, ____, ____, ____, -7
Finding the 𝑛𝑡ℎ Term Given Two Terms:
a) Find the 6th term of the arithmetic sequence with…
𝑎9 = 120 𝑎𝑛𝑑 𝑎14 = 195
1st - Find the common difference
Let 𝑎𝑛 = 𝑎14 , 𝑎𝑛𝑑 𝑎1 = 𝑎9 𝑎𝑛𝑑
replace 1 with 9
b) Find the 5th term of the arithmetic sequence with…
𝑎8 = 85 𝑎𝑛𝑑 𝑎14 = 157
1st - Find the common difference
Lastly…Complete:
68 is the _______ term of -2, 3, 8…
Homework (Day 1) p.648/ 21 – 32