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Difference between revisions of "Manuals/calci/ARITHMETICSERIES"

(Created page with "<div style="font-size:30px">'''ANGLE (deg,by,till)'''</div><br/> *<math>deg</math> is the starting angle value in degree *<math> by </math> is the skip value.")
 
 
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<div style="font-size:30px">'''ANGLE (deg,by,till)'''</div><br/>
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<div style="font-size:30px">'''ARITHMETICSERIES (Start,Difference,Numbers,OnlyNth)'''</div><br/>
−
*<math>deg</math> is the starting angle value in degree
+
*<math>Start</math> is the starting value  
−
*<math> by </math> is the skip value.
+
*<math> Difference </math> is the difference value of the series.
 +
*<math>Numbers</math> is the positive real number.
 +
 
 +
==Description==
 +
*This function gives the Arithmetic series of the numbers.
 +
*An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant  d.
 +
*Therefore, for k>1,
 +
<math>a_{k}=a_{(k-1)}+d=a_{(k-2)}+2d=...=a_{1}+d(k-1)</math>. 
 +
*The sum of the sequence of the first n terms is then given by
 +
<math>S_{n} = \sum_{k=1}^n a_k</math>
 +
 
 +
==Examples==
 +
#ARITHMETICSERIES(10,3,6) = 10 13 16 19 22 25
 +
#ARITHMETICSERIES(200,13/7,5) = 200 201.85714285714286 203.71428571428572 205.57142857142858 207.42857142857142
 +
#ARITHMETICSERIES(33,-7,8) = 33 26 19 12 5 -2 -9 -16
 +
#Sn=(a,r,n) => a*(1-r^n) / (1- r); Sn(1,4,5) = 341
 +
#Sn=(a,r,n) => a*(1-r^n) / (1- r); Sn#; Sn(1,4..10,5)
 +
{| id="TABLE3" class="SpreadSheet blue"
 +
|- class="even"
 +
| class=" " |
 +
|a   
 +
|r   
 +
|n   
 +
|Sn
 +
 
 +
|- class="odd"
 +
| class=" " |
 +
|1   
 +
|4   
 +
|5   
 +
|341
 +
|- class="even"
 +
| class="  " |
 +
|1   
 +
|5   
 +
|5   
 +
|781
 +
 
 +
|- class="odd"
 +
| class="  " |
 +
|1   
 +
|6   
 +
|5   
 +
|1555
 +
 
 +
|- class="even"
 +
| class="  " |
 +
|1   
 +
|7   
 +
|5   
 +
|2801
 +
 
 +
|- class="odd"
 +
| class="  " |
 +
|1   
 +
|8   
 +
|5   
 +
|4681
 +
 
 +
|- class="even"
 +
| class="  " |
 +
|1   
 +
|9   
 +
|5   
 +
|7381
 +
 
 +
|- class="odd"
 +
| class="  " |
 +
|1   
 +
|10   
 +
|5   
 +
|1111
 +
|}
 +
</div>
 +
 
 +
==Related Videos==
 +
 
 +
{{#ev:youtube|v=Uy_L8tnihDM|280|center|Arithmetic Series}}
 +
 
 +
==See Also==
 +
*[[Manuals/calci/SERIESSUM| SERIESSUM]]
 +
*[[Manuals/calci/SUM| SUM]]
 +
*[[Manuals/calci/PRODUCT| PRODUCT]]
 +
 
 +
==References==
 +
*[http://www.purplemath.com/modules/series4.htm Arithmetic series]
 +
 
 +
 
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
 
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 01:30, 30 June 2021

ARITHMETICSERIES (Start,Difference,Numbers,OnlyNth)


  • is the starting value
  • is the difference value of the series.
  • is the positive real number.

Description

  • This function gives the Arithmetic series of the numbers.
  • An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant d.
  • Therefore, for k>1,
 .
  • The sum of the sequence of the first n terms is then given by

 

Examples

  1. ARITHMETICSERIES(10,3,6) = 10 13 16 19 22 25
  2. ARITHMETICSERIES(200,13/7,5) = 200 201.85714285714286 203.71428571428572 205.57142857142858 207.42857142857142
  3. ARITHMETICSERIES(33,-7,8) = 33 26 19 12 5 -2 -9 -16
  4. Sn=(a,r,n) => a*(1-r^n) / (1- r); Sn(1,4,5) = 341
  5. Sn=(a,r,n) => a*(1-r^n) / (1- r); Sn#; Sn(1,4..10,5)
a r n Sn
1 4 5 341
1 5 5 781
1 6 5 1555
1 7 5 2801
1 8 5 4681
1 9 5 7381
1 10 5 1111

Related Videos

Arithmetic Series

See Also

References


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