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 nth term of a geometric sequence?

Back

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

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 the sequence.

Front

Find the 5th term of the geometric sequence: 3, 6, 12, 24,...

Back

The 5th term is 48.

Front

If the first term of a geometric sequence is 5 and the common ratio is 3, what is the 4th term?

Back

The 4th term is 135.

Front

Is the sequence 1, 2, 4, 8, 16,... geometric?

Back

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

Front

What is the common ratio for the sequence: 81, 27, 9, 3,...?

Back

The common ratio is 1/3.

Front

Determine if the sequence 10, 20, 30, 40,... is geometric.

Back

No, it is not geometric; it is an arithmetic sequence.

Front

What does 'r' represent in a geometric sequence?

Back

'r' represents the common ratio.

Front

If a geometric sequence has a common ratio of -2, what is the 3rd term if the first term is 4?

Back

The 3rd term is -16.