Flashcard on Patterns and Sequences

Front

What is a finite sequence?

Back

A finite sequence is a sequence that has a specific number of terms and terminates at a certain point.

Front

What is an infinite sequence?

Back

An infinite sequence is a sequence that continues indefinitely without terminating.

Front

How can all sequences be considered functions?

Back

All sequences can be considered functions because each term number is assigned one time to a term value, and no term numbers repeat.

Front

What is a term of a sequence?

Back

A term of a sequence is defined as an individual number, figure, or letter that marks each ordered component within the sequence.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (or term numbers) for which the function is defined.

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

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

Back

The nth term of an arithmetic sequence 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

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

Back

The nth term of a geometric sequence 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 sum of the first n terms of an arithmetic sequence?

Back

The sum of the first n terms of an arithmetic sequence can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.