Difference between revisions of "Manuals/calci/ARITHMETICSERIES"
Jump to navigation
Jump to search
| (6 intermediate revisions by 2 users not shown) | |||
| Line 10: | Line 10: | ||
<math>a_{k}=a_{(k-1)}+d=a_{(k-2)}+2d=...=a_{1}+d(k-1)</math>. | <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 | *The sum of the sequence of the first n terms is then given by | ||
| − | <math>S_{n} = sum_{ | + | <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.
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
- 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)
| 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
See Also
References