Geometric Sequences

Front

What is a geometric sequence?

Back

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 constant factor between consecutive terms in a geometric sequence.

Front

How do you find the common ratio of a geometric sequence?

Back

Divide any term by the previous term.

Front

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

Back

12 (3 × 4 = 12).

Front

Is the sequence {5, 15, 45, 135, ...} arithmetic, geometric, or neither?

Back

Geometric.

Front

What is the formula for the nth term of a geometric sequence?

Back

a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

If a geometric sequence has a common ratio of 1/2, what happens to the terms?

Back

The terms decrease and approach zero.

Front

What is the first term of the geometric sequence {64, 16, 4, ...}?

Back

64.

Front

If the common ratio of a geometric sequence is 3, what is the fifth term if the first term is 2?

Back

486 (2 * 3^4 = 486).

Front

What is the relationship between geometric sequences and exponential functions?

Back

Geometric sequences can be represented by exponential functions.