Arithmetic and Geometric Sequences

Front

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 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.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the nth term of an Arithmetic Sequence?

Back

The nth term (a_n) 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

How do you find the nth term of a Geometric Sequence?

Back

The nth term (a_n) 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) is the constant amount that each term increases or decreases by in an Arithmetic Sequence.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in a Geometric Sequence?

Back

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

Tags

CCSS.HSF.BF.A.2

Front

Find the 11th term of the sequence: 1, -2, 4, -8, ...

Back

The 11th term is 1024.

Tags

CCSS.HSF.BF.A.2

Front

Find the next three terms of the sequence: 4, 24, 144, 864, ...

Back

The next three terms are 5184, 31104, 196624.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio of the sequence: -4, -12, -36, -108, ...

Back

The common ratio is r=3.

Tags

CCSS.HSF.BF.A.2

Front

Find the 32nd term of the sequence: 34, 37, 40, 43, ...

Back

The 32nd term is 127.

Tags

CCSS.HSF.BF.A.2