# Series and Sequence

A series is the value (sum) obtained when all the terms of a sequence are added up. For example, "1, 2, 3, 4" is a sequence, with terms "1", "2", "3", and "4"; the corresponding series is the sum "1 + 2 + 3 + 4", and the value of the series is 10.

A sequence, aka progression, is an ordered list of numbers. The numbers in this ordered list are called "elements" or "terms".

While some sequences are simply random values, other sequences have a definite pattern that is used to arrive at the sequence's terms. Two such sequences are the arithmetic and geometric sequences.

An arithmetic sequence is one that has a sequence of values follows a pattern of adding a fixed or constant amount from one term to the next.

vCalc's Series and Sequence contains equations that compute the sum of the terms of a sequence.

### Parent Categories:

## Series and Sequence Equations

- `sum_(k=1)^n1/([p + (k-1)q](p+kq))`
- `sum_(k=1)^naq^(k-1)`
- `sum_(k=1)^nk^p`
- `sum_(x=0)^n(r^x sin(x alpha))`
- `sum_(x=1)^n cos(x alpha)`
- `sum_(x=1)^n sin(x alpha)`
- `sum_(x=1)^n x`
- `sum_(x=1)^n(2x-1)`
- `sum_(x=1)^n(a +(x-1)d)`
- `sum_(x=1)^n(x^2)`
- `sum_(x=1)^n(x^3)`
- `sum_(x=1)^n(x^4)`
- Arithmetic Series- Alternative Sum-of-Terms Formula
- Arithmetic Series-Last Term Formula_Copy
- Fibonacci Term
- Sum of Infinite Geometric Series_Copy
- Table of Integrals, Series and Products, 0dot14 - 2
- `sum_(k=0) ^ (n-1) (a+kr)`
- `sum_(x=0)^n(r^x cos(x alpha))`
- Fibonacci Sequence
- Golden Ratio Sequence
- Infinite Geometric Series
- Liouville's Number
- Sum_014-3
- Sum_014-4
- Sum_0_142