NAME
DATE
10-1
PERIOD
Practice
Sequences, Series, and Sigma Notation
Find the specified term of each sequence.
n2 − n
1. ninth term, an = −
n
2. fourth term, a 1 = 10, a n = (−1) a n − 1 + 5
4n − 18
4
-5
Determine whether each sequence is convergent or divergent.
n
(−1)
2n − 1
4. a n = −
divergent
Lesson 10-1
3. 20, 18, 14, 8, …
convergent
Find the indicated sum for each sequence.
5. seventh partial sum of 13, 22, 31, 40, …
6. S 4 of a n = 2(3.5)
n
280
417.375
Find each sum.
5
3
7. ∑ (n 2 − 2 n)
-6
8. ∑ (2n - 3)
n=3
0
n=0
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write a recursive formula and an explicit formula for each sequence.
9. -4, -1, 4, 11, …
1 3 9 27
, − , − , −, …
10. −
2 2 2
2
1
a1 = −
, a n = 3a n − 1; for n ≥ 2
a 1 = −4, a n = a n − 1 + 2n − 1;
2
1
an = −
(3) n − 1
2
for n ≥ 2; an = n 2 − 5
Write each series in sigma notation. The lower bound is given.
11. 3 + 6 + 9 + 12 + 15; n = 1
12. 24 + 19 + 14 + … + (–1); n = 0
5
5
∑ 3n
∑ (24 - 5n)
n=1
n=0
13. SAVINGS Kathryn started saving quarters in a jar. She began by
putting two quarters in the jar the first day and then she increased the
number of quarters she put in the jar by one additional quarter each
successive day.
a. Use sigma notation to represent the total number of quarters Kathryn
had after 10 days.
10
∑ (n + 1)
n=1
b. Find the sum represented in part a. 65
Chapter 10
7
Glencoe Precalculus