Unit 7 Exam Review Sequences and Series.

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Presentation transcript:

Unit 7 Exam Review Sequences and Series

Formulas (will be given on exam) Sequence Series Arithmetic Geometric Finite Infinite

Question 1 Determine if the sequence is arithmetic or geometric. Describe the pattern. Find the next three terms: 13, 15, 17, 19, …

Question 2 Determine if the sequence is arithmetic or geometric. Describe the pattern. Find the next three terms: 4, 8, 16, 32, …

Question 3 Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.

Question 4 Write a recursive formula for the sequence 8, 10, 12, 14, 16, … . Then find the next term.

Question 5 Write an explicit formula for the sequence 7, 2, -3, -8, -13, … . Then find a14.

Question 6 Is the sequence arithmetic? If so, identify the common difference. 13, 20, 27, 34, …

Question 7 Find the missing term of the arithmetic sequence: 22, ___, 34, …

Question 8 Is the sequence geometric? If so, identify the common ratio. 6, 12, 24, 48, …

Question 9 Write the explicit formula for the sequence. Then find the fifth term in the sequence. a1 = 3, r = - 3

Question 10 Find the missing term of the geometric sequence: 45, ____ 1620, …

Question 11 A large asteroid crashed into a moon of a planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic sequence 26, 44, 62, 80, … . Find the total distance that the projectile traveled in seven seconds.

Question 12 Use summation notation to write the series 49 + 54 + 59 + … for 14 terms.

Question 13 8 For the series Σ4n , find the number of terms in the series. n = 1

Question 14 Evaluate the infinite geometric series. Round to the nearest hundredth if necessary. 8 + 4 + 2 + … 1 + 0.1 + 0.01 + …

Use summation notation to write the series Question 15 Use summation notation to write the series 35 + 39 + 43 + 47 +… for 8 terms.

Question 16 Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on. If the daily wage keeps doubling, what will your total income be for working 31 days?