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.
- 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 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
- 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
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