Arithmetic and Geometric Sequences

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What is an arithmetic sequence?

Back

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

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in the sequence.

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CCSS.HSF.BF.A.2

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term 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

Front

What is a geometric sequence?

Back

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

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in the sequence.

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CCSS.HSF.BF.A.2

Front

How do you find the nth term of a geometric sequence?

Back

The nth term 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.

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CCSS.HSF.BF.A.2

Front

What is the formula to calculate the 10th term of the arithmetic sequence: 4, 7, 10, 13, 16?

Back

The 10th term is calculated as: a_10 = 4 + (10-1) * 3 = 31.

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CCSS.HSF.BF.A.2

Front

If a tree grows by 3 cm every 3 days, what is the height after 12 days?

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After 12 days, the height will be: 2 + (12/3) * 3 = 14 cm.

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CCSS.HSF.BF.A.2

Front

What is the common difference in the sequence: 4, 0, -4, -8, -12?

Back

The common difference is -4.

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CCSS.HSF.BF.A.2

Front

How do you identify the common ratio in the sequence: 81, 27, 9, 3, 1?

Back

The common ratio is found by dividing any term by the previous term: 27/81 = 1/3.

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