Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

Van een Rekenkundige Rij t₁, t₂, ... met verschil v = 5, is s₁₀₀ − s₉₉ = 1000. De waarde van de term t₁₀₁ is	A. 1000
	B. 1005
	C. 1010
	D. 1500
	E. minder dan 1000

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Translation in E N G L I S H

For the arithmetic sequence t₁, t₂, ... with common difference d=5 is s₁₀₀ − s₉₉ = 1000. Find the 101th term of this arithmetic sequence ( s_n = the sum of the first n terms )	A. 1000
	B. 1005
	C. 1010
	D. 1500
	E. less than 1000

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\left.\begin{matrix}s_{100}=t_1+t_2+t_3+t_4+\cdots t_{98}+t_{99}+t_{100}& \\s_{99}=t_1+t_2+t_3+t_4+\cdots t_{98}+t_{99}\qquad& \\\\\end{matrix}\right\}s_{100}-s_{99}=t_{100} \; ! !\\ t_{101}=t_{100}+v=1000+5=1005$