Sequences and Series

Gives the constant difference between any term and its predecessor in an arithmetic progression.

Gives the nth term of an arithmetic progression with first term a and common difference d.

Gives the nth term from the end of a finite arithmetic progression having last term l.

Gives the sum of the first n terms of an arithmetic progression given the common difference or the last term.

Gives the nth term of any sequence from the formula for the sum of its first n terms.

Gives the condition for three real numbers a, b, and c to form an arithmetic progression.

Gives the arithmetic mean of two numbers a and b.

Gives the common difference when inserting n arithmetic means between a and b.

Gives the nth term of a geometric progression with first term a and common ratio r.

Gives the sum of the first n terms of a geometric progression.

Gives the sum to infinity of an infinite geometric progression when the absolute common ratio is less than 1.

Gives the condition for three non-zero numbers a, b, and c to form a geometric progression.

Gives the geometric mean of two positive real numbers a and b.

Gives the common ratio when inserting n geometric means between positive numbers a and b.

Gives the sum of the first n positive integers.

Gives the sum of the squares of the first n positive integers.

Gives the sum of the cubes of the first n positive integers.