Nth Term

InternetIsBeautiful

A couple of days back I stumbled upon this website: nth-test.com. Nth Test is an nth-child and nth-of-type tester. It requires you to input an n^th term of a sequence and it displays the sequence formed corresponding to that n^th term. What it basically does is that it calculates the Arithmetic Progression (A.P.) for that n^th term. So for example if we input 2n-1, it will output the progression: 1, 3, 5, 7 ... on a tabular block in an interactive way. It makes calculating the n^th child easier.

So I came out with Nth Term that does the exact opposite of the above explained concept. It takes the sequence (Arithmetic Progression) as input and displays the n^th term for it. It also extends the input sequence and highlights the numbers on a table.

So suppose you need the n^th term for the following sequence: 5, 9, 13 ...
All you need to do is type the numbers in the input form separated by commas and you will get the n^th term and the extended sequence for the input.

I have defined n as a Natural Number, i.e. n ∈ N. So n can only take values from the set: { 1, 2, 3, 4, ... }. You may enter values of n and check if the output series is correct in the table.

For n = 1, 4n+1 = 5
For n = 2, 4n+1 = 9
For n = 3, 4n+1 = 13
For n = 4, 4n+1 = 17

... and so on.

You may have noticed a smiley to the left of the input form. A smile : ) means a hit, i.e. the n^th term has been found. A sad face : ( means the series is not an A.P. and when it is waiting for a proper input by you, it would display an "indifferent" smiley : |