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 in the sequence by the previous term (r = a_n / a_(n-1)).

Front

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

Back

The variable 'r' represents the common ratio of the geometric sequence.

Front

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

Back

The second term is 6 (3 * 2).

Front

Given the geometric sequence 5, 15, 45, ..., what is the common ratio?

Back

The common ratio is 3 (15 / 5 = 3).

Front

Is the sequence 1, 2, 4, 8, ... a geometric sequence?

Back

Yes, it is a geometric sequence with a common ratio of 2.

Front

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

Back

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

Front

Find the common ratio for the sequence: 10, 30, 90, ...

Back

The common ratio is 3 (30 / 10 = 3).

Front

If a geometric sequence has a common ratio of -1, what can be said about its terms?

Back

The terms of the sequence will alternate in sign.

Front

What is the common ratio of the sequence: 4, -16, 64, -256, ...?

Back

The common ratio is -4.