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 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

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 9th term?

Back

The 9th term is 768.

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

Is the sequence -432, 72, -12, 2 a geometric sequence?

Back

Yes, it is a geometric sequence.

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is constant.

Front

What is the common ratio of a geometric sequence with terms 4, 8, 16?

Back

The common ratio is 2.

Front

Given the rule a_n = 10(2)^(n-1), what is the common ratio?

Back

The common ratio (r) is 2.

Front

Find the first four terms of the sequence defined by a_n = 4(5)^(n-1).

Back

The first four terms are 4, 20, 100, 500.

Front

What is the 5th term of a geometric sequence with a first term of 1 and a common ratio of 3?

Back

The 5th term is 81.