Manuals/calci/ARITHMETICSERIES

ARITHMETICSERIES (Start,Difference,Numbers,OnlyNth)

• $Start$ is the starting value
• $Difference$ is the difference value of the series.
• $Numbers$ 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,

$a_{k}=a_{(k-1)}+d=a_{(k-2)}+2d=...=a_{1}+d(k-1)$.  

• The sum of the sequence of the first n terms is then given by

$S_{n}=\sum _{k=1}^{n}a_{k}$

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

• SERIESSUM
• SUM
• PRODUCT

References

• Arithmetic series

• List of Main Z Functions

• Z3 home