Unit 1: Sequences (Review)
Unit Review
Topics Covered:
1. Arithmetic Sequences
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2. Arithmetic Series
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3. Geometric Sequences
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4. Finite Geometric Series:
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5. Infinite Geometric Series:
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Homework:
Worksheet and p. 60 #12,13
Examples:
1. Find in the following arithmetic sequence: 36, 29, 22, …
2. Insert two numbers between -13 and 47 so the four numbers form an arithmetic sequence.
3. In an arithmetic sequence, the fourth term is 29 and the eleventh term is 50. Find the first 4 terms
4. A display of cans has 36 cans in the bottom row. Each row has 5 fewer cans than the previous row.
a) How many rows are in the display?
b) How many cans are in the top row?
c) How many cans are in the display?
5. Determine the sum of the first 10 terms in the following arithmetic series:
31 + 38 + 45 + …
6. Determine the sum of the following arithmetic series:
11 + 15 + 19 + … + 435
7. What is t12 in the following geometric sequence?
3, -6, 12, ….
8. A car is currently worth $18,000. Its price depreciates by 6% per year. How much will it be worth in 5 years?
9. Insert two numbers between 7 and 56 so the four numbers form a geometric sequence.
10. In a geometric sequence, the first term is 5. The sum of the first 4 terms is 200 and the sum of the first 5 terms is 605. What are the first 5 terms of the sequence?
11. The sum of the first 10 terms in a geometric sequence with common ratio 4 is 699,050. Determine the first term.
12. The hour hand on a clock points at 12 o’clock. It is rotated 70o, then 100o, then 50o, then 25o, and so on. To which number will the hour hand converge?
13. Are the following infinite series convergent or divergent?
a) 10 – 15 + 22.5 – 33.75 + …. b) –18 + 15 – 12.5 + ….