Arithmetic vs Geometric Sequences

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

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 difference in an arithmetic sequence?

Back

The common difference is the fixed amount that each term in an arithmetic sequence increases or decreases by.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the fixed number that each term in a geometric sequence is multiplied by to get the next term.

Front

Identify the common difference in the sequence: 5, 8, 11, 14...

Back

The common difference is 3.

Front

Identify the common ratio in the sequence: 3, 6, 12, 24...

Back

The common ratio is 2.

Front

Which of the following is an arithmetic sequence? 2, 4, 6, 8 or 1, 2, 4, 8?

Back

2, 4, 6, 8 is an arithmetic sequence.

Front

Which of the following is a geometric sequence? 1, 3, 9, 27 or 1, 2, 3, 4?

Back

1, 3, 9, 27 is a geometric sequence.

Front

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

Back

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

Front

What is the formula for 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 and r is the common ratio.