Geometric Sequences

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

Given the sequence 2, 6, 18, 54, what is the common ratio?

Back

3

Tags

CCSS.HSF.BF.A.2

Front

How do you find the next term in a geometric sequence?

Back

Multiply the last term by the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

If the first term a1 = 4 and the common ratio r = 2, what is the second term a2?

Back

8

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CCSS.HSF.BF.A.2

Front

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

Back

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

If a geometric sequence has a first term of 5 and a common ratio of 3, what is the 4th term?

Back

135

Tags

CCSS.HSF.BF.A.2

Front

What does a1 represent in a geometric sequence?

Back

a1 represents the first term of the sequence.

Tags

CCSS.HSF.BF.A.2

Front

In the sequence defined by a_n = 3 * 4^(n-1), what is a5?

Back

768

Tags

CCSS.HSF.BF.A.2

Front

If the common ratio is 1/2, what happens to the terms of the sequence?

Back

The terms decrease and approach zero.