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 expressed as 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

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

Back

The common ratio (r) can be found by dividing any term by the previous term: r = a_n / a_(n-1).

Front

Given the sequence 3, 9, 27, what is the common ratio?

Back

The common ratio is 3, since 9/3 = 3 and 27/9 = 3.

Front

What is the common ratio for the geometric sequence: 64, 16, 4?

Back

The common ratio is 1/4.

Front

If a geometric sequence has a first term of 5 and a common ratio of 2, what is the 4th term?

Back

The 4th term is 5 * 2^(4-1) = 5 * 8 = 40.

Front

What is the explicit formula for the geometric sequence: 2, -12, 72?

Back

The explicit formula is a_n = 2 * (-6)^(n-1).

Front

How do you determine the nth term of a geometric sequence?

Back

To determine the nth term, use the formula a_n = a_1 * r^(n-1) with known values of a_1 and r.

Front

What is the common ratio for the geometric sequence: 2, -12, 72?

Back

The common ratio is -6.

Front

If a geometric sequence has a rule a_n = 7(1/2)^(n-1), what is the common ratio?

Back

The common ratio is 1/2.