I often have to generate a polynomial sequence so I created this simple online utility that does it for me. It lets you generate however many polynomial series numbers you need in any base. It works in the browser and is powered by alien technology from the future.

## Polynomial Progression Generator Options

## Polynomial Progression Generator Examples (click to try!)

^{0}to be 0 and therefore we have the following series – p₀ = 2, p₁ = 2 + 3¹, p₂ = 2 + 3², p₃ = 2 + 3³, p₄ = 2 + 3⁴, …. We generate the series up to p₂₀ and separate polynomial terms by commas.

2, 5, 11, 29, 83, 245, 731, 2189, 6563, 19685, 59051, 177149, 531443, 1594325, 4782971, 14348909, 43046723, 129140165, 387420491, 1162261469

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

0; 4; 16; 64; 256; 1024; 4096; 16384; 65536; 262144

-256 -254 -252 -248 -240 -224 -192 -128 0 256 768 1792

1 1.1 1.01 1.001 1.0001 1.00001 1.000001 1.0000001 1.00000001 1.000000001

10 1 11 1 11 1 11 1 11 1

## How Does This Polynomial Progression Generator Work?

This polynomial series generator works entirely in your browser and is written in JavaScript. It implements a sequence generator that uses the polynomial formula pₙ = a + bⁿ, where `pₙ`

is the n-th sequence term, `a`

is the fixed constant value (can be specified in options), and `b`

is the common-ratio (also can be changed in options). It uses the variable name `fixedValue`

for `a`

and the variable name `commonRatio`

for `b`

. Both values are created from strings by constructing `new BigNumber()`

objects. It uses an array `polynomials`

to store sequence elements and adds the first `fixedValue`

element to it via `var polynomials = [fixedValue]`

. Then, it runs a `for`

loop `count`

times (given in options), with the start value `var i = 1`

and an increment of 1 (via `i++`

). It calculates the polynomial formula via two BigNumber library methods. The first one, `pow()`

, raises `commonRatio`

to the power `i`

and the second one, `plus()`

, adds `fixedValue`

to the number. Then it converts the polynomial term to the selected base via `toString(base)`

function and `push()`

es it to the `polynomials`

array. When the loop finishes, all values are joined together via `join(sep)`

function, where `sep`

is the output separator (specified in options).

### Created by Browserling

This polynomial progression generator was created by me and my team at Browserling. Behind the scenes, it's actually powered by our web developer tools that are used by millions of people every month. Browserling itself is an online cross-browser testing service powered by alien technology. Check it out!

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