Arithmetic & Geometric Sequence 3rd

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 (d = a_{n+1} - a_n).

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 (r = a_{n+1} / a_n).

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence is a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula for a geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Given the sequence 4, 9, 14, 19, ... what is the common difference?

Back

The common difference is 5.

Front

Given the sequence 4, 16, 64, ... what is the common ratio?

Back

The common ratio is 4.

Front

Given the sequence -2, -4, -8, -16, ... what is the common ratio?

Back

The common ratio is 2.

Front

What is the explicit formula for the sequence 8, 14, 20, 26, ...?

Back

The explicit formula is a_n = 6n + 2.