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 is the factor by which we multiply each term to get the next term in the sequence.

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 and r is the common ratio.

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 4th term?

Back

The 4th term is 3 * 2^(4-1) = 3 * 8 = 24.

Front

Is the sequence 2, 4, 8, 16 a geometric sequence?

Back

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

Front

What is the common ratio of the sequence 10, 5, 2.5?

Back

The common ratio is 0.5 (or 1/2).

Front

What is a_5 for the sequence a_n = 3 * 4^(n-1)?

Back

a_5 = 3 * 4^(5-1) = 3 * 256 = 768.

Front

Determine if the sequence 1, 3, 9, 27 is geometric.

Back

Yes, it is geometric with a common ratio of 3.

Front

What is the 6th term in a geometric sequence with a first term of 5 and a common ratio of 3?

Back

The 6th term is 5 * 3^(6-1) = 5 * 243 = 1215.

Front

If a geometric sequence has a common ratio of 1/3, what happens to the terms?

Back

The terms decrease and approach zero as n increases.