Geometric/Arithmetic 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.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The nth term (a_n) of an arithmetic sequence can be calculated using the formula: a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

Tags

CCSS.HSF.BF.A.2

Front

What is a geometric sequence?

Back

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

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The nth term (a_n) of a geometric sequence can be calculated 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

Front

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

Back

The common difference (d) in an arithmetic sequence can be found by subtracting any term from the subsequent term: d = a_(n+1) - a_n.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The common ratio (r) in a geometric sequence can be found by dividing any term by the previous term: r = a_(n+1) / a_n.

Tags

CCSS.HSF.BF.A.2

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What is the common difference in the sequence 5, 10, 15, 20, ...?

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The common difference is 5.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in the sequence 3, 9, 27, 81, ...?

Back

The common ratio is 3.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of an arithmetic sequence is 4 and the common difference is 2, what is the 5th term?

Back

The 5th term is 12.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 4th term?

Back

The 4th term is 54.

Tags

CCSS.HSF.BF.A.2