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

To find the common ratio, divide any term in the sequence by the previous term (r = a_n / a_(n-1)).

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CCSS.HSF.BF.A.2

Front

What is the common ratio of the sequence 4, -16, 64, -256?

Back

The common ratio is -4.

Tags

CCSS.HSF.BF.A.2

Front

Is the sequence -4, -12, -36, -108 geometric?

Back

Yes, it is geometric because each term is multiplied by -3 to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

Is the sequence 9, 99, 999, 9999 geometric?

Back

No, it is not geometric because the ratio between consecutive terms is not constant.

Tags

CCSS.HSF.BF.A.2

Front

What are the first four terms of the sequence defined by a_n = 4(5)^(n-1)?

Back

The first four terms are 4, 20, 100, 500.

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 expressed as 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 3 and the common ratio is 2, what is the 5th term?

Back

The 5th term is 3 * 2^(5-1) = 48.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The sum S_n of the first n terms can be calculated using the formula S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

Tags

CCSS.HSA.SSE.B.4

Front

What happens to the terms of a geometric sequence if the common ratio is between 0 and 1?

Back

The terms will decrease and approach zero as n increases.

Tags

CCSS.HSF.BF.A.2