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11.1 Mathematical Patterns
11.2 Arithmetic Sequences
11.3 Geometric Sequences
11.4 Arithmetic Series
11.5 Geometric Series
100
Describe the pattern formed and find the next three terms of the following sequence. 4, 8, 16, 32, 64, ...
What is: Each term is twice the preceding term (x2). 128, 256, 512
100
Is the given sequence arithmetic? If so, find the common difference. 100, 10, 1, 0.1, ...
Not arithmetic.
100
A sequence is considered geometric if there is a _____ ratio between consecutive terms.
common
100
Evaluate the series of the finite sequence, 100, 99, 98, ..., 95
585
100
Evaluate the finite series for the specified number of terms. 7 - 35 + 175 - ...; n = 5
3647
200
Describe the pattern formed and find the next three terms of the following sequence. 1/2, 1/4, 1/8, 1/16, 1/32, ...
Each term is half the preceding term (x1/2). 1/64, 1/128, 1/256
200
Find the 32nd term of the sequence, 213, 201, 189, 177, ...
-159
200
Is the sequence geometric? If so find the common ratio and the next two terms. 10, 15, 22.5, 33.75, ...
Yes. r = 1.5. 50.625, 75.9375
200
The following sequence has eight terms. Evaluate the related series. -3.5, -1.25, 1, ..., 12.25
35
200
Decide whether the infinite geometric series diverges or converges. State whether the series has a sum. 1/4 + 1/2 + 1 + 2 + ...
Diverges, Has no sum.
300
Write a recursive formula for the sequence. Then find the next term. 40, 20, 10, 5, 5/2, ...
an = (an-1)/2 where a1=40. Next term: 5/4
300
Find the missing term of the arithmetic sequence, 101, ___ , -115
-7
300
Find the missing term of the geometric sequence. 12, ___ , 3
6
300
Use summation notation to write the arithmetic series for the specified number of terms. 7 + 14 + 21 + ...; n = 15
Lower Limit: 1, Upper Limit: 15, Explicit Formula: 7n
300
Evaluate the finite series for the specified number of terms. 4 + 12 + 36 + ...; n = 6
1456
400
Is the given formula explicit or recursive? Then find the first five terms of the sequence. an = 5n
Explicit. 5, 10, 15, 20, 25
400
Find the arithmetic mean an of the given terms. an-1 = 3/5, an+1 = 1
4/5
400
Is the sequence arithmetic, geometric, or neither? Then find the next two terms. 2, 1, 0.5, 0.25, ...
Geometric. 0.125, 0.0625
400
Is the following list a sequence or series? Finite or infinite? 4/3, 7/3, 10/3, 13/3, 16/3, ...
Infinite Sequence
400
Evaluate the infinite geometric series. 3 + 1 + 1/3 + 1/9 + ...
9/2 or 4.5
500
Write an explicit formula for the sequence. Then find a12. 4, 5, 6, 7, 8, ...
an = n + 3, a12 = 15
500
Find the 17th term of the sequence, a18 = 18, d = -4
22
500
Write the explicit formula for the sequence. Then find the first five terms. a1 = 1024, r = 0.5
an = 1024(0.5)^(n-1). 1024, 512, 256, 128, 64
500
For each sum, find the number of terms, the first term, and the last term. Then evaluate the series. WRITE ON BOARD
6 terms, a3 = 4, a8 = -1, Sn = 9
500
Determine whether the series is arithmetic or geometric. Then evaluate the finite series for the specified number of terms. -5 + 25 - 125 + 625 - ...; n = 9
Geometric. -1,627, 605