Sequences

Front

What is a sequence?

Back

A sequence is an ordered list of numbers that follow a specific pattern or rule.

Front

What is an arithmetic sequence?

Back

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

Front

What is the common difference in an arithmetic sequence?

Back

The common difference (d) is the fixed amount added to each term to get the next term in an arithmetic sequence.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term (a_n) 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 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 ratio in a geometric sequence?

Back

The common ratio (r) is the factor by which we multiply each term to get the next term in a geometric sequence.

Front

How do you find the nth term of a geometric sequence?

Back

The nth term (a_n) 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.

Front

What is the explicit formula for the arithmetic sequence 12, 10, 8, 6, ...?

Back

a_n = 12 + (n - 1)(-2)

Front

Given a_1 = 5 and d = 2, find a_6.

Back

a_6 = 5 + (6 - 1) * 2 = 15.

Front

Is the sequence 3, 9, 15, 22, ... arithmetic, geometric, or neither?

Back

Neither (no common difference OR common ratio).