Arithmetic & Geometric Sequences

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What is an arithmetic sequence?

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An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

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CCSS.HSF.BF.A.2

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What is a geometric sequence?

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A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

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CCSS.HSF.BF.A.2

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How do you find the common difference in an arithmetic sequence?

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The common difference is found by subtracting any term from the subsequent term (d = a(n+1) - a(n)).

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CCSS.HSF.BF.A.2

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How do you find the common ratio in a geometric sequence?

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The common ratio is found by dividing any term by the previous term (r = a(n) / a(n-1)).

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CCSS.HSF.BF.A.2

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What is the formula for the nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence can be found using the formula: a(n) = a(1) + (n-1)d, where a(1) is the first term and d is the common difference.

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CCSS.HSF.BF.A.2

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What is the formula for the nth term of a geometric sequence?

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The nth term of a geometric sequence can be found using the formula: a(n) = a(1) * r^(n-1), where a(1) is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

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Determine if the sequence 17, 9, 1, -7 is arithmetic or geometric.

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The sequence is arithmetic because the common difference is -8.

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CCSS.HSF.BF.A.2

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Determine if the sequence 78, 785, 7855, 78555 is arithmetic or geometric.

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The sequence is neither arithmetic nor geometric because the differences and ratios are not constant.

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CCSS.HSF.BF.A.2

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If a population decreases by 3% each year, how do you calculate the population after n years?

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Use the formula: P(n) = P(0) * (1 - r)^n, where P(0) is the initial population, r is the rate of decrease, and n is the number of years.

Tags

CCSS.HSF.BF.A.2

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What is the 15th term of the sequence a(n) = -3n + 50?

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The 15th term is 5.

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CCSS.HSF.BF.A.2