T9 Review: 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 common ratio (r) in a geometric sequence?

Back

The common ratio (r) can be found by dividing any term by the previous term, i.e., r = a_n / a_(n-1).

Front

Given the sequence 64, -16, 4, -1, what is the common ratio?

Back

r = -1/4.

Front

What is the explicit formula for a geometric sequence?

Back

Front

If the first term of a geometric sequence is 15 and the common ratio is 25, what is the explicit formula?

Back

Front

Back

Front

What does the letter 'r' represent in a geometric sequence?

Back

'r' represents the common ratio.

Front

If a geometric sequence has a common ratio of -1/4, what is the second term if the first term is 64?

Back

The second term is 64 * (-1/4) = -16.

Front

How can you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio between consecutive terms is constant.

Front

What is the relationship between the common ratio and the terms of a geometric sequence?

Back

The common ratio determines how each term in the sequence is derived from the previous term.