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

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

Back

The common ratio (r) can be found by dividing any term in the sequence by the previous term, i.e., r = a_n / a_(n-1).

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The nth term 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

If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 5th term?

Back

The 5th term is calculated as a_5 = 2 * 3^(5-1) = 2 * 81 = 162.

Tags

CCSS.HSF.BF.A.2

Front

What are the next three terms of the geometric sequence 5, 15, 45, ...?

Back

The next three terms are 135, 405, 1215.

Tags

CCSS.HSF.BF.A.2

Front

In the sequence 1, 4, 16, 64, what is the common ratio?

Back

The common ratio is 4, as each term is multiplied by 4 to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is constant.

Tags

CCSS.HSF.BF.A.2

Front

What is the 11th term of the geometric sequence -3, 6, -12, 24?

Back

The 11th term is -3,072.

Tags

CCSS.HSF.BF.A.2

Front

What is the next term in the geometric sequence 2, 6, 18, 54?

Back

The next term is 162.

Tags

CCSS.HSF.BF.A.2

Front

If a geometric sequence has a common ratio of 1/2 and the first term is 8, what is the 4th term?

Back

The 4th term is 8 * (1/2)^(4-1) = 8 * (1/2)^3 = 8 * 1/8 = 1.

Tags

CCSS.HSF.BF.A.2