Adv. Math 1 Arithmetic vs. 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. This difference is called the common difference.

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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 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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How do you find 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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What is the common difference in the sequence 3, 7, 11, 15?

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The common difference is 4, as each term increases by 4.

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CCSS.HSF.BF.A.2

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What is the common ratio in the sequence 2, 6, 18, 54?

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The common ratio is 3, as each term is multiplied by 3 to get the next term.

Tags

CCSS.HSF.BF.A.2

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If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the 10th term?

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The 10th term is 23.

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CCSS.HSF.BF.A.2

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If the first term of a geometric sequence is 4 and the common ratio is 2, what is the 5th term?

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The 5th term is 64.

Tags

CCSS.HSF.BF.A.2

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Describe the sequence 100, 50, 25, ...

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It is a geometric sequence with a common ratio of 1/2.

Tags

CCSS.HSF.BF.A.2

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What is the formula for the nth term of the sequence -10, -3, 4, 11?

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The formula is a_n = -17 + 7n.

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CCSS.HSF.BF.A.2