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 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

Find the 5th term of the geometric sequence 4, 8, 16, 32.

Back

The 5th term is 64.

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 find the nth term of a geometric sequence?

Back

Use the formula a_n = a_1 * r^(n-1) to find the nth term.

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

Tags

CCSS.HSA.SSE.B.4