Algebra and Trigonometry

Mathematics

Quiz 10 :

Sequences, Series and Probability

Quiz 10 :

Sequences, Series and Probability

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Find the sum of the arithmetic sequence img that satisfies the stated conditions. img
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C

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Use the binomial theorem to expand and simplify. img
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B

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Evaluate the expression. 6!0!
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E

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Bode's sequence, defined by img can be used to approximate distances of planets from the sun. These distances are measured in astronomical units, with 1 AU = 93,000,000 mi. For example, the third term corresponds to earth and the fifth term to the minor planet Ceres. Find the 4th term of the sequence.
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A rubber ball is dropped from a height of 50 feet. If it rebounds approximately two-thirds the distance after each fall, use an infinite geometric series to approximate the total distance the ball travels.
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Find the third term of the geometric sequence whose first two terms are 4 and 16.
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Use the binomial theorem to expand and simplify. img
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Use the binomial theorem to expand and simplify. img
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Find the number. img
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Without expanding completely, find the term in the expansion of the expression that contains img . img
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Use the principle of mathematical induction to find the equivalent expression for every positive integer n. img
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Find the third term of the sequence: img is the number of decimal places in img .
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Evaluate the expression. img
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Find the sum. img
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Find the third term of the recursively defined infinite sequence. img
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Use the principle of mathematical induction to find the factor of the expression. img Hint: img
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If seven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.
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Find the fourth partial sum for the given sequence. img
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A company is to distribute $29,000 in bonuses to its top five salespeople. The fifth salesperson on the list will receive $4,600, and the difference in bonus money between successively ranked salespeople is to be constant. Find the bonus for each salesperson.
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Express the sum in terms of n. img (Hint: Use the theorem on sums to write the sum as img . Next, use the following formulas img and the theorem on the sum of a constant.)
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