i hav thiught a lot about the problem but at the end i was not even able to mave an inch forword .the problem is: we hav to develop a program that make user input a series and then will calculate the misiong term.

ex:

1>4,6,9, ,14,16,19,...
then the answer should be 11

Sounds to me like he needs to elaborate more on exactly what the assignment wants, unless there's a magic algorithm out there that can predict the readings of geiger counters. The two series he showed are pretty easy, but are they the only ones?

Well , Abhi According to the Question That You are asking. You need the computer to determine the a sequence from user input. This is not definable as the user may type in anything . If thats not the case and you are given an arithmetic progression when 2 numbers are given and told to find the next sequence. Then you can take the difference between the 2 numbers and then go on adding it.

1. Arithmetic: When a number is added constantly. 2, 6, 10, 14, 18, 22

Here the rule is +2 after every term.

2. Geometric: When a number is multiplied constantly. 4, 8, 16, 32, 64, 128, 256

Here the rule is *2 after every term.

Find the algorithm by using this formula:

1. For Arithmetic succesions: (An - A1) - (n-1)

2. For Geometric succesions: Sqrt"n-1"(An/A1)

For these formulas to work you need to have the user introduce the first term, and the last term.

Hope this helps. :)

Edit:

I re-read your problem and you could solve it using this mind-set:

Have the program use the first term as A1 and the second term as An and use the appropiate formula to find the rule of the succesion. The it's a matter of simply using the rule on the first term "n" number of times the users requests.