Summation of a series when provided with First and Last Numbers only...

Summation of a series when provided with First and Last Numbers only...
Dear Forum,

I need to get Summation of all the numbers, however I only have the First and the Last number...

I am not a mathematician and not aware of the mathematical formula..

For Ex:-

I have the Starting number as 21 and the next number is 42,63,so on so forth...now the last number is 21 X 13 = 271

Now, as the Starting and Ending numbers keep on changing as well as the difference ( i.e 13 ) also changes and so its difficult to get summation.

The answer I am looking for 21+42+63+x+x+x+x+x+x+x+271
But without knowing the other numbers except 21 nd 271,is there a way of getting the Summation?"

21 * 13 = 273

If A1 contains the first number in an arithmetic series and A2 contains the last, then the sum is =A2 / A1 * (A1 + A2) / 2

Originally Posted by shg

21 * 13 = 273

If A1 contains the first number in an arithmetic series and A2 contains the last, then the sum is =A2 / A1 * (A1 + A2) / 2

Shg,

These are the numbers under consideration..

290
267
243
220
198
175
152
130
108
86
64
43
21

I tried your approach , however I got a different answer...
The answer which should come is 1996~ or close to it...

As the difference between the numbers ranges from 21,22and 23...

Originally Posted by shg

That's a bunch of random numbers, not a series. If you only have the first and last, who could know what the numbers in between are?

Yes, you are absolutely right but I have the numbers for now but in the future I would be getting only the First and Last number but this has to be right..is there any other way?

Originally Posted by shg

Here's a finite arithmetic series: 21, 42, 63. The total is 126.

Change the middle number to 43. It's no longer an arithmetic series, and the sum is now 127.

The first and last number tell you the interior numbers (and therefore the sum) ONLY if you know it's an arithmetic sequence beginning with the first number.

I think you are right...I will follow your approach..and come back wit a better explanation...
This is the gorundwork for something more complex and i needed to use this approach...

I am actually tryn to get to the Present value when I need to the Future Value, Rate of Interest and No of Installments...but I will start a new thread for that...

Let me think for this issue and come back 2mrw..thanks for the help till now...