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In Excel Fill Series if you input 23, 132, 2
then 31.33333333, 20.83333333, 10.33333333, -0.166666667, -10.66666667....is generated

and if you input 13, 16, 17
then 19.33333, 21.33333, 23.33333, 25.33333.. is generated as shown below

What is the algorithm for number generation?

Series 1 Series 2

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  • $\begingroup$ Welcome to Puzzling SE! Can you please be more clear in your problem? What's the question? Where's that sequence from? $\endgroup$ – leoll2 Apr 19 '15 at 17:48
  • $\begingroup$ I am asking about how the given series is formed as in image. If 23,132, 2, then how 31.3333 is generated as next number? $\endgroup$ – Deepak Apr 19 '15 at 18:13
  • $\begingroup$ And what is 20.83? The next number of the sequence? $\endgroup$ – leoll2 Apr 19 '15 at 18:14
  • $\begingroup$ yes numbers in the given image are automatically generated by excel if we give 23,132,2 as input for Fill Series. $\endgroup$ – Deepak Apr 19 '15 at 18:19
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The sequences are a linear extrapolation of the 3 initial points as follows:

  • the starting point is Backcalc2 which is the average of the 3 initial points
  • the Increment is the average of Actual2-Actual1 and Actual3-Actual2

Sequence

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  • $\begingroup$ Nice answer, but Could you please further explain how you got the Backcalc 62.83333? Thanks for you help $\endgroup$ – Deepak Apr 20 '15 at 4:39
  • $\begingroup$ @Deepak - OK. Start at 52.33333. Going down the column, continue to subtract 10.5. Then going back up the same column, each number is increasing by 10.5. So add 10.5 to 52.33333 to get 62.83333. $\endgroup$ – Len Apr 20 '15 at 6:26
  • $\begingroup$ You algorithm satisfies correctly if we give input as three numbers. But if we give 4 numbers as input 23,1541,42,21 then this sequence is generated 30.5,-120, -270.5, -421, -571.5, -722, -872.5... Could you please explain the algorithm for this? $\endgroup$ – Deepak Apr 20 '15 at 8:34
  • $\begingroup$ To match Excel with 4 or more input numbers, a proper linear regression calculation needs to be done. The input numbers can be entered into this calculator. Then the Excel fill numbers can be matched by using the best fit equation. $\endgroup$ – Len Apr 21 '15 at 5:02

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