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.

Tags

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 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 4, -16, 64, -256, ...?

Back

r = -4

Tags

CCSS.HSF.BF.A.2

Front

What is the next term in the geometric sequence 4, 16, 64, ...?

Back

256

Tags

CCSS.HSF.BF.A.2

Front

Is the sequence 2, 4, 12, 48,... 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 next 3 terms in the geometric sequence 512, 256, 128, ...?

Back

64, 32, 16

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio for the geometric sequence 2, 4, 8, 16, ...?

Back

r = 2

Tags

CCSS.HSF.BF.A.2

Front

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

Back

15

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

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

Back

1.

Tags

CCSS.HSF.BF.A.2