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

How do you find the first four terms of a geometric sequence given the first term and the common ratio?

Back

To find the first four terms, start with the first term and multiply by the common ratio for each subsequent term. For example, if a₁ = 10 and the common ratio is 3, the terms are: 10, 30, 90, 270.

Front

What is the explicit formula for a geometric sequence?

Back

Front

What is the recursive rule for a geometric sequence?

Back

The recursive rule for a geometric sequence is defined as: a₁ = first term; a_n = a_n-1 * r, where r is the common ratio.

Front

How do you identify the common ratio in a geometric sequence?

Back

The common ratio can be found by dividing any term by the previous term. For example, in the sequence 64, 16, 4, the common ratio is 1/4 (16/64 or 4/16).

Front

What is the difference between a geometric sequence and an arithmetic sequence?

Back

In a geometric sequence, each term is multiplied by a constant (common ratio), while in an arithmetic sequence, each term is added to a constant (common difference).

Front

How do you find the next term in a geometric sequence?

Back

To find the next term, multiply the last known term by the common ratio. For example, if the last term is 90 and the common ratio is 3, the next term is 90 * 3 = 270.

Front

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

Back

Front

How do you derive the explicit formula from a recursive formula?

Back

Front

What is the explicit formula for the sequence 25, 125, 225, 325?

Back