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 formula for the nth term of a geometric sequence?

Back

The formula for the nth term of a geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

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

Back

To find the common ratio, divide any term by the previous term (r = a_n / a_(n-1)).

Front

Is the sequence 2, 4, 12, 48 a geometric sequence?

Back

No, this sequence is not geometric because the ratio between consecutive terms is not constant.

Front

Find the 11th term of the geometric sequence: 64, -32, 16, -8, ...

Back

The 11th term is -0.0625.

Front

What is the explicit rule for the geometric sequence: 125, 25, 5, ...?

Back

The explicit rule is t(n) = 625(1/5)^n.

Front

What is the common ratio of the sequence: 64, -32, 16, -8, ...?

Back

The common ratio is -1/2.

Front

What is the first term of the geometric sequence: 64, -32, 16, -8, ...?

Back

The first term is 64.

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 5th term?

Back

The 5th term is 48.

Front

What is the general rule for the sequence: 64, -32, 16, -8, ...?

Back

The general rule is 64(-1/2)^(n-1).