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Finite Arithmetic–Geometric Sum

Sum a sequence whose terms combine an arithmetic factor with a geometric weight.

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01 Your input
02 Your result
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FormulaSum = r===1 ? n*(2*a+(n-1)*d)/2 : a*(1-r**n)/(1-r)+d*(r-n*r**n+(n-1)*r**(n+1))/(1-r)**2
Sources and model references

Made for real tasks

  • Sum a sequence whose terms combine an arithmetic factor with a geometric weight.
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Worked example

Inputs

Initial arithmetic term
2 number
Arithmetic increment
1 number
Geometric ratio
0.5 number
Term count
10 count

Expected results

Sum
5.974609375 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter initial arithmetic term, arithmetic increment, geometric ratio, term count.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "a": 2,
  "d": 1,
  "r": 0.5,
  "n": 10
}

Accuracy and scope

Terms are (a+k*d)*r^k for k=0…n−1. Near r=1, direct closed-form subtraction can lose precision.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.