Arithmetic and 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

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

Back

The common difference can be found by subtracting any term from the term that follows it.

Front

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

Back

The common ratio can be found by dividing any term by the term that precedes it.

Front

What are the first 4 terms of an arithmetic sequence with a common difference of 5 if the first term is 2?

Back

2, 7, 12, 17

Front

What are the first 4 terms of a geometric sequence with a common ratio of 3 if the first term is 1?

Back

1, 3, 9, 27

Front

If the first term of an arithmetic sequence is 10 and the common difference is -2, what are the first 4 terms?

Back

10, 8, 6, 4

Front

If the first term of a geometric sequence is 4 and the common ratio is 2, what are the first 4 terms?

Back

4, 8, 16, 32

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.