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. This difference is called the common difference (d).

Tags

CCSS.HSF.BF.A.2

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

Back

The nth term (a_n) 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.

Tags

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 (r).

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The nth term (a_n) 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

Front

What is the common difference in an arithmetic sequence?

Back

The common difference (d) in an arithmetic sequence is the constant amount that each term increases or decreases by from the previous term.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric sequence?

Back

The common ratio (r) in a geometric sequence is the constant factor by which each term is multiplied to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

Find the 22nd term of the arithmetic sequence: 5, 8, 11, ...

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68

Tags

CCSS.HSF.BF.A.2

Front

Identify the pattern in the sequence: 3, 6, 9, 12.

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The pattern is a multiple of 3.

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CCSS.3.OA.D.9

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What are the next two terms of the sequence: 4, 7, 10, 13?

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16 and 19.

Tags

CCSS.HSF.BF.A.2

Front

Which formula is used to find the recursive equation for arithmetic sequences?

Back

a_n = a_(n-1) + d.

Tags

CCSS.HSF.BF.A.2