Geometric Sequence

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 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 does a_1 represent in a geometric sequence?

Back

a_1 represents the first term of the geometric sequence.

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 5 * 3^(4-1) = 5 * 27 = 135.

Front

What are the next three terms in the geometric sequence: 2, 6, 18, ...?

Back

The next three terms are 54, 162, 486.

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 formula for the sum of the first n terms of a geometric sequence?

Back

The sum S_n of the first n terms is given by S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

Front

If a geometric sequence has a common ratio of 1/2 and the first term is 16, what is the 5th term?

Back

The 5th term is 16 * (1/2)^(5-1) = 16 * (1/16) = 1.

Front

What is the 3rd term in the geometric sequence: 81, 27, ...?

Back

The 3rd term is 9.