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How to calculate the increasing point if known variables are sum of total increase points and the first point.

For example, I have the first number of 1000, and I have 37 points until the last one. Sum of all points should be 107300.

So I have to calculate what number I need to add to every increasing point.

Example:

1st increasing point: 1000 + 100 = 1100
2nd increasing point: 1100 + 100 = 1200
...
37th increasing point: = 4600 + 100 = 4700

I need to know how to calculate this increasing number (100), as I only know the sum of all points is 107300 and the first point is 1000.

EDIT: I'll explain with my chart example. I have an xy axis in which y represents total bookings and x represents month. So I have set goal that I would like to have 107300 bookings in that 37 months. Currently I have 1000 bookings, and I need to calculate for what number my bookings needs to be increased for every month so I could reach 107300 bookings in 37 months.

Drazen
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  • If you also know the starting value (which you have not specified explicitly), then the step value is just a difference between the final and the initial value, divided by a number of steps. – CiaPan Apr 14 '19 at 21:03
  • I don't have final value, I have the sum of all points which is 107300 and the first point which is 1000. – Drazen Apr 14 '19 at 21:06
  • I'm afraid I don't get what the 'point' is here. The problem seems purely arithmetic to me, but 'points' suggest some geometric interpretation or backgroung. Could you rephrase it to use arithmetic notions only? Or explain the precise meaning of 'points'…? – CiaPan Apr 14 '19 at 21:19
  • I'll explain with my chart example. I have an xy axis in which y represents total bookings and x represents month. So I have set goal that I would like to have 107300 bookings in that 37 months. Currently I have 1000 bookings, and I need to calculate for what number my bookings needs to be increased for every month so I could reach 107300 bookings in 37 months. Is it clear now? :) – Drazen Apr 14 '19 at 21:38
  • When providing clarification, please click on the tiny edit and use MathJax and improve the body of the post instead of commenting. – Lee David Chung Lin Apr 14 '19 at 21:57
  • @LeeDavidChungLin thanks for the tips, I'm new so still getting to know with :) – Drazen Apr 15 '19 at 07:27

1 Answers1

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I still don't have a clear idea what you mean. As far as I could get, you have a finite artihmetic sequence: $$\begin{align}a_1& \\a_2&=a_1+r,\\ a_3&=a_1+2r,\\ \vdots\\ a_n&=a_1+(n-1)r.\end{align}$$ Is that correct?

And you know $a_1$ and $n$, as well as the sum $S_n=a_1+a_2+\ldots+a_n=\sum_{i=1}^n a_i.$
And you want to find the value of $r$, right?

The sum of a finite arithmetic sequence is $$S_n = \sum\limits_{i=1}^n a_i = n\cdot\frac {a_1+a_n}2$$ so $$S_n = n\cdot\frac {2a_1+(n-1)r}2$$

Now you just need to plug in the known values of $n, a_1$ and $S_n$ and solve the simple equation for unknown $r$.

CiaPan
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