Lesson 6.2 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.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio (r) is the factor by which we multiply each term to get the next term in the sequence.

Front

If a₃ = 224 and r = -½, how do you find a₈?

Back

Use the formula a_n = a₁ * r^(n-1). First, find a₁ using a₃ = a₁ * r^(3-1). Then calculate a₈.

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 = a₁ * r^(n-1), where a₁ is the first term and r is the common ratio.

Front

Find the common ratio for the geometric sequence: 2, -12, 72.

Back

The common ratio is -6, calculated as -12/2 = -6 and 72/-12 = -6.

Front

What are the next three terms of the sequence: 2, -12, 72?

Back

The next three terms are -432, 2592, -15552.

Front

Write the explicit rule for the geometric sequence: 2, -12, 72.

Back

The explicit rule is a_n = 2(-6)^(n-1).

Front

What type of function does a geometric sequence model?

Back

A geometric sequence models an exponential function.

Front

How do you find the nth term if you know a₃ and r?

Back

Use the formula a_n = a₃ * r^(n-3) to find any term in the sequence.

Front

If a₁ = 5 and r = 3, what is a₄?

Back

a₄ = 5 * 3^(4-1) = 5 * 27 = 135.