1. For each of the sequences below, find the pattern that makes the sequence and then find the 5th and 6th terms.
a. 12, 14, 16, 18, ...
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b. 4, 8, 16, 32, ...
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c. 7, 15, 31, 63, ...
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d. 16, 8, 4, 2, ...
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e. 4, 9, 16, 25, ...
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f. 14, 16, 20, 28, ...
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g. 2.5, 3, 3.5, 4, ...
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h. -4, 8, -16, 32...
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2. Given the following formulas for the general term of a sequence, find the first three terms, t1, t2 and t3
a. < 5n − 2>
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b. < 2n3 >
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c. < n / 2 >
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d. < 4n − 3>
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e.
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f. < (n − 1)(n + 4 >
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g. t n = n2 + 1 |
h. t n =
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3. Given the following first terms and the recursive function, find the next three terms.
First term
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Recursive function
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Next three terms
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a.
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t 1 = 5
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t n+1 = t n + 2
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5, _ , _ , _ |
b.
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t 1 = 1
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t n+1 = 3t n
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1, _ , _ , _ |
c.
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t 1 = 2
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t n+1 = 3t n − 2
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2, _ , _ , _ |
d.
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t 1 = 3
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t n+1 = (t n)2 + 2
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3, _ , _ , _ |
e.
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t 1 = 12
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t n+1 =3 − t n
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12, _ , _ , _ |
4. Evaluate the following sums:
5. Write the following sums in sigma notation:
a. 12 + 13 + 14 + 15 +16 + 17
b. 2t3 +2t4 +2t5 +2t6
c. 9 + 16 + 25 + 36
d. 4 + 6 + 8 + 10 + 12 + 14
e. -3 + 6 − 9 + 12 − 15 + 18 − 21
f. 17 + 26 + 37 + ... + 145
6. Draw a graph of the following sequences and say whether the sequence is:
(i) increasing, decreasing or oscillating
(ii) Convergent or divergent (if it is convergent, give the limit)
a
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b
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< n+ 5 >
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c
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d
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<(-1)n(n + 1)>
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e
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< n2 − 3n >
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f
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t(n) = 3
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