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 in a geometric sequence?

Back

The common ratio (r) can be found by dividing any term by the previous term: r = t(n) / t(n-1).

Front

Given the sequence: 125, 25, 5, .... What is the common ratio?

Back

1/5

Front

What is the zeroth term of a geometric sequence?

Back

The zeroth term can be found by dividing the first term by the common ratio raised to the power of the index: t(0) = t(1) / r.

Front

Given the sequence: 125, 25, 5, .... What is the zeroth term?

Back

625

Front

Write the explicit equation for the geometric sequence: 6, 24, 96...

Back

Front

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

Back

The nth term can be expressed as: t(n) = t(1) * r^(n-1), where t(1) is the first term and r is the common ratio.

Front

Find the next three terms: 4, 12, 36, 108, ...

Back

324, 972, 2916.

Front

What is the common ratio of the geometric sequence 3, 12, 48, ...?

Back

4.

Front

If the first term of a geometric sequence is 10 and the common ratio is 2, what is the 5th term?

Back

The 5th term is 10 * 2^(5-1) = 160.