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 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 formula for the nth term of an arithmetic sequence?

Back

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

a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

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

Back

The common difference (d) is found by subtracting any term from the term that follows it: d = a_n - a_(n-1).

Front

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

Back

The common ratio (r) is found by dividing any term by the term that precedes it: r = a_n / a_(n-1).

Front

What does a_1 represent in a sequence?

Back

a_1 represents the first term of the sequence.

Front

What is the difference between an arithmetic and a geometric sequence?

Back

In an arithmetic sequence, each term is added by a constant (common difference), while in a geometric sequence, each term is multiplied by a constant (common ratio).

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 4th term?

Back

The 4th term is a_4 = 3 * 2^(4-1) = 3 * 8 = 24.