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 general formula for the n-th term of a geometric sequence?

Back

The n-th 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

Given the sequence 64, -32, 16, -8, what is the common ratio?

Back

The common ratio is r = -1/2.

Tags

CCSS.HSF.BF.A.2

Front

What is the explicit formula for the sequence 5, 15, 45, ...?

Back

The explicit formula is a_n = 5(3)^(n-1).

Tags

CCSS.HSF.LE.A.2

Front

How do you find the 11th term of a geometric sequence?

Back

To find the 11th term, use the formula a_n = a_1 * r^(n-1) with n=11.

Tags

CCSS.HSF.BF.A.2

Front

What are the next three terms in the sequence 4, 12, 36, 108?

Back

The next three terms are 324, 972, 2916.

Tags

CCSS.HSF.BF.A.2

Front

What is the first term of the geometric sequence 64, -32, 16, -8?

Back

The first term (a_1) is 64.

Tags

CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 5 and the common ratio is 3, what is the 4th term?

Back

The 4th term is a_4 = 5 * 3^(4-1) = 5 * 27 = 135.

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