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.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 4 and the common ratio is 2, what are the first four terms?

Back

4, 8, 16, 32.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The nth term 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 explicit formula for the geometric sequence 3, 6, 12, 24?

Back

a_n = 3 * 2^(n-1).

Tags

CCSS.HSF.BF.A.2

Front

Calculate the common ratio for the sequence 5, 15, 45, 135.

Back

The common ratio is 3.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for the sum of the first n terms of a geometric sequence?

Back

The sum S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

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CCSS.HSA.SSE.B.4

Front

If a geometric sequence has a common ratio of -2, what is the second term if the first term is 5?

Back

The second term is -10.

Tags

CCSS.HSF.BF.A.2

Front

What is the relationship between the common ratio and the terms of a geometric sequence?

Back

Each term is obtained by multiplying the previous term by the common ratio.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 10 and the common ratio is 1/2, what is the 5th term?

Back

The 5th term is 10 * (1/2)^(5-1) = 10/16 = 5/8.

Tags

CCSS.HSF.BF.A.2