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 a geometric sequence.

Front

If the first term of a geometric sequence is 5 and the common ratio is 3, what are the first four terms?

Back

5, 15, 45, 135

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula is a(n) = a(0) * r^n, where a(0) is the first term, r is the common ratio, and n is the term number.

Front

What is the recursive formula for a geometric sequence?

Back

The recursive formula is a(n) = r * a(n-1), where r is the common ratio.

Front

How do you find the nth term of a geometric sequence?

Back

Use the explicit formula: a(n) = a(0) * r^n.

Front

What does 'a(0)' represent in a geometric sequence?

Back

a(0) represents the first term of the geometric sequence.

Front

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

Back

The terms will decrease and approach zero as n increases.

Front

What is the 5th term of the geometric sequence: 2, 6, 18, ...?

Back

The 5th term is 162.

Front

In the sequence 81, 27, 9, ..., what is the common ratio?

Back

The common ratio is 1/3.