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 (r = a_n / a_(n-1)).

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio of the sequence 2, 6, 18, 54, ...?

Back

The common ratio is 3.

Tags

CCSS.HSF.BF.A.2

Front

Is the sequence 5, 10, 20, 40, ... geometric?

Back

Yes, the sequence is geometric with a common ratio of 2.

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) 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

Find the common ratio for the geometric sequence: 3, 9, 27, 81, ...

Back

The common ratio is 3.

Tags

CCSS.HSF.BF.A.2

Front

Determine if the sequence 1, 1/2, 1/4, 1/8, ... is geometric.

Back

Yes, it is geometric with a common ratio of 1/2.

Tags

CCSS.HSF.BF.A.2

Front

What are the next three terms in the geometric sequence: 4, 12, 36, ...?

Back

The next three terms are 108, 324, 972.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 5 and the common ratio is -2, what is the 4th term?

Back

The 4th term is 5 * (-2)^(4-1) = 5 * (-2)^3 = -40.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio of the sequence: 64, -16, 4, -1, ...?

Back

The common ratio is -1/4.

Tags

CCSS.HSF.BF.A.2