Arithmetic/Geometric Sequences

Front

What is an arithmetic sequence?

Back

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 fixed amount that each term increases or decreases by, denoted as 'd'.

Front

What is a geometric sequence?

Back

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 fixed number that each term is multiplied by to get the next term, denoted as 'r'.

Front

What is the explicit formula for an arithmetic sequence?

Back

a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference.

Front

What is the explicit formula for a geometric sequence?

Back

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

Front

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

Back

Use the explicit formula: a_n = a_1 + (n-1)d.

Front

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

Back

Use the explicit formula: a_n = a_1 * r^(n-1).

Front

What is a recursive formula?

Back

A formula that defines each term of a sequence using the preceding term(s).

Front

Can the recursive formula be used without knowing the previous term?

Back

No, the recursive formula requires knowledge of the previous term.