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 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

What are the next 3 terms in the geometric sequence: 81, 27, 9, ...

Back

The next 3 terms are 3, 1, and 1/3.

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

What is the 3rd term of the geometric sequence defined by a_1 = 2 and r = 5?

Back

The 3rd term is 50.

Front

If a geometric sequence has a common ratio of 1/2, what happens to the terms?

Back

The terms will decrease and approach zero as they continue.

Front

Find the common ratio for the geometric sequence: 10, 30, 90, ...

Back

The common ratio is 3.