mathematics

What is a Sequence?

A function whose domain is a set of numbers, like {1, 2, 3,…, n}.

What is an Arithmetic Sequence?

A sequence where the difference between consecutive terms is constant.

How is the common difference (d) found in an arithmetic sequence?

Subtracting any two consecutive terms in the sequence. Denoted as d.

What is the formula for finding the nth term of an arithmetic sequence?

an = a1 + (n - 1)d

What is a Sequence?

A function whose domain is a set of numbers, like {1, 2, 3,…, n}.

What is an Arithmetic Sequence?

A sequence where the difference between consecutive terms is constant.

How is the common difference (d) found in an arithmetic sequence?

Subtracting any two consecutive terms in the sequence. Denoted as d.

What is the formula for finding the nth term of an arithmetic sequence?

an = a1 + (n - 1)d

What are Arithmetic Means?

Terms between two nonconsecutive terms in an arithmetic sequence.

What is an Arithmetic Series?

The sum of the terms in an arithmetic sequence.

What is the formula for the sum of an arithmetic series?

Sn = \frac{n}{2}(a1 + a_n). Use when the first and last terms are known.

What is the formula for the sum of an arithmetic series if the last term is not given?

Sn = \frac{n}{2}[2a1 + (n-1)d]. Use when the last term is not known.

What is a Geometric Sequence?

A sequence where each term is found by multiplying the previous term by a constant ratio.

How is the common ratio (r) found in a geometric sequence?

Dividing any term by its preceding term. Denoted as r.

What is the formula for the nth term of a geometric sequence?

an = a1r^{(n-1)}

What are the characteristics of Arithmetic Sequences?

Constant difference (addition/subtraction), linear variation.

What are the characteristics of Geometric Sequences?

Constant ratio (multiplication/division), exponential variation.

What are Geometric Means?

The term(s) between any two nonconsecutive terms of a geometric sequence.

What is a Geometric Series?

The sum of the terms of a geometric sequence.

What is the formula for a Finite Geometric Series?

Sn = \frac{a1(1 - r^n)}{1 - r}

What is the formula for an Infinite Geometric Series?

S = \frac{a_1}{1 - r}