Geometric and Arithmetic 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 an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.

Front

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

Back

To find the common ratio, divide any term by the previous term in the sequence.

Front

How do you find the common difference in an arithmetic sequence?

Back

To find the common difference, subtract any term from the previous term in the sequence.

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

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.

Front

What is the common ratio of the geometric sequence -1, 6, -36, 216, ...?

Back

-6

Front

What is the 8th term in the geometric sequence 3, 9, 27, 81, ...?

Back

6,561

Front

Identify the common difference in the sequence 97, 86, 75, 64, ...

Back

-11

Front

What is the common ratio of the sequence 5, 25, 125, ...?

Back

5