series and sequences Math 1 Plus

What is a sequence?

A sequence is an ordered list of numbers. Each number in a sequence is called a term.

What is an arithmetic sequence?

An arithmetic sequence is a list of numbers where the difference between each term and the one before it is always the same. This constant difference is called the common difference (d).

How do you find the n^{th} term of an arithmetic sequence?

The formula for the n^{th} term of an arithmetic sequence is:an = a1 + (n-1)d - an is the n^{th} term - a1 is the first term - n is the term number - d is the common difference

What is a geometric sequence?

A geometric sequence is a list of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number. This constant multiplier is called the common ratio (r).

How do you find the n^{th} term of a geometric sequence?

The formula for the n^{th} term of a geometric sequence is:an = a1 \bullet r^{n-1} - an is the n^{th} term - a1 is the first term - n is the term number - r is the common ratio

What is a series?

A series is the sum of the terms of a sequence.

What is an arithmetic series?

An arithmetic series is the sum of the terms of an arithmetic sequence.

How do you find the sum of the first n terms of an arithmetic series?

The formula for the sum of the first n terms of an arithmetic series is:Sn = \frac{n}{2}(a1 + an) - Sn is the sum of the first n terms - n is the number of terms - a1 is the first term - an is the n^{th} (last) term

What is a geometric series?

A geometric series is the sum of the terms of a geometric sequence.

How do you find the sum of the first n terms of a geometric series?

The formula for the sum of the first n terms of a finite geometric series is:Sn = a1 \frac{(1 - r^n)}{(1 - r)} - Sn is the sum of the first n terms - a1 is the first term - n is the number of terms - r is the common ratio

How do you find the n^{th} term of a geometric sequence?

The formula for the n^{th} term of a geometric sequence is:an = a1 \bullet r^{n-1} - an is the n^{th} term - a1 is the first term - n is the term number - r is the common ratio

What is a series?

A series is the sum of the terms of a sequence.

What is an arithmetic series?

An arithmetic series is the sum of the terms of an arithmetic sequence.

How do you find the sum of the first n terms of an arithmetic series?

The formula for the sum of the first n terms of an arithmetic series is:Sn = \frac{n}{2}(a1 + an) - Sn is the sum of the first n terms - n is the number of terms - a1 is the first term - an is the n^{th} (last) term

What is a geometric series?

A geometric series is the sum of the terms of a geometric sequence.

How do you find the sum of the first n terms of a geometric series?

The formula for the sum of the first n terms of a finite geometric series is:Sn = a1 \frac{(1 - r^n)}{(1 - r)} - Sn is the sum of the first n terms - a1 is the first term - n is the number of terms - r is the common ratio