Ch. 12 Study Guide
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Formulas:
1. Arithmetic Sequence: 𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑
𝑎1 +𝑎𝑛
)
2
2. Arithmetic Series: 𝑆𝑛 = 𝑛(
3. Geometric Sequence: 𝑎𝑛 = 𝑎1 (𝑟)𝑛−1
1−𝑟 𝑛
)
1−𝑟
4. Finite Geometric Series: 𝑆𝑛 = 𝑎1 (
5. Infinite Geometric Series: 𝑆 =
𝑎1
1−𝑟
Define:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Arithmetic Sequence
Common Difference
Arithmetic Series
Geometric Sequence
Common Ratio
Finite Geometric Series
Infinite Geometric Series
Sigma; Σ
Partial Sum
Explain the difference between a sequence and a series.
How can you determine whether a sequence is
arithmetic or geometric?
How can you tell if an infinite series has a sum?
Tell whether the sequence is arithmetic, geometric, or
neither. Explain why.
1.
2.
3.
4.
5.
6.
-10, -7, -5, -2, 0, …
0.5, 1, 1.5, 2, 2.5, 3, …
20, 10, 5, 2.5, 1.25, …
1, -2, -5, -8, -11, …
0.2, 0.6, 1.8, 5.4, 16.2, …
-5, 10, 20, 40, 80, …
Write a rule for the nth term of the arithmetic
sequence. Then find 𝒂𝟐𝟎 .
1. 1, 4, 7, 10, 13, …
2. 5, 11, 17, 23, 29, …
Write a rule for the nth term of the geometric
sequence. Then find 𝒂𝟕 .
1. 4, 2, 1, 0.5, …
2. 1, -4, 16, -64, …
Write a rule for the nth term of the arithmetic
sequence.
1.
2.
3.
4.
𝑎16 = 52; 𝑑 = 5
𝑎12 = −3, 𝑑 = −7
𝑎5 = 15, 𝑎9 = 24
𝑎2 = 17, 𝑎11 = 35
Write a rule for the nth term of the geometric
sequence.
1.
2.
3.
4.
𝑎2
𝑎3
𝑎3
𝑎2
= 6; 𝑟 = 2
= 75, 𝑟 = 5
= 10, 𝑎6 = 270
= −40, 𝑎4 = −10
Find the sums of the arithmetic series using both the
series formula and sigma.
1. 2 + 6 + 10 + … + 58
2. -1 + 4 + 9 + … + 34
Find the sums of the infinite geometric series, if it
exists, using both the series formula and sigma.
1.
2
3
2.
4
15
2
9
− +
4
2
2
− +
27
81
20
+ 9 + 27 +
⋯
100
+⋯
81
A regional soccer tournament had 64 participating
teams. In the first round of the tournament, 32 games
are played. In each successive round, the number of
games played is decreased by one half.
1. Find a rule for the number of games played in
the nth round. For what value of n does your
rule make sense?
2. Find the total number of games played in the
regional soccer tournament using both the
series formula and sigma.
Write the repeating decimal as a fraction in lowest
terms.
1.
2.
3.
4.
32.3232…
0.444…
0.2777…
0.625625625…