Manuals/calci/ARITHMETICSERIES

ARITHMETICSERIES (Start,Difference,Numbers,OnlyNth)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Start} is the starting value
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 11111 Related Videos Arithmetic Series See Also SERIESSUM SUM PRODUCT References Arithmetic series List of Main Z Functions Z3 home