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?

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The common ratio (r) can be found by dividing any term by the previous term: r = a_n / a_(n-1).

Tags

CCSS.HSF.BF.A.2

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula for a geometric sequence is 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

Given the sequence 3, -12, 48, -192, what is the common ratio?

Back

The common ratio is -4.

Tags

CCSS.HSF.BF.A.2

Front

What is the 9th term of the geometric sequence 4, 8, 16, 32?

Back

The 9th term is 1,024.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

To calculate the nth term, use the formula a_n = a_1 * r^(n-1).

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio for the sequence 28, 14, 7, 3.5?

Back

The common ratio is 1/2.

Tags

CCSS.HSF.BF.A.2

Front

If a geometric sequence has a first term of 6 and a common ratio of 2, what is the 12th term?

Back

The 12th term is 12,288.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

The sum S_n of the first n terms is given by 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 less than 1?

Back

If the common ratio is less than 1, the terms of the sequence will decrease and approach zero.

Tags

CCSS.HSF.BF.A.2