Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\large\boldsymbol{\frac {7} {5},\;\frac {14} {15},\; \frac {28} {45}, ... }$ is een meetkundige rij. De som van de eerste vier termen bedraagt	A. $\boldsymbol{\frac {91} {8} }$
	B. $\boldsymbol{\frac {91} {54} }$
	C. $\boldsymbol{\frac {91} {27} }$
	D. $\boldsymbol{\frac {65} {27} }$
	E. $\boldsymbol{\frac {98} {27} }$

[ 4-4499 - op net sinds 9.1.15-()-13.1.2025 ]

Translation in E N G L I S H

sum first 4 terms IN CONSTRUCTION

Oplossing - Solution

$\\s_4=t_1.\frac{1-q^n}{1-q}=\frac75.\frac{1-\left(\frac23\right)^4}{1-\frac23}=\frac75.\frac{1-\frac{16}{81}}{\frac13}\\=\frac75.\left(3-\frac{16}{27}\right)=\frac75.\frac{81-16}{27}=\frac75.\frac{65}{27}=\frac{7.13}{27}=\frac{91}{27}$

\(\large\boldsymbol{\frac {7} {5},\;\frac {14} {15},\; \frac {28} {45}, ... }\) is een meetkundige rij. De som van de eerste vier termen bedraagt	A. \(\boldsymbol{\frac {91} {8} }\)
	B. \(\boldsymbol{\frac {91} {54} }\)
	C. \(\boldsymbol{\frac {91} {27} }\)
	D. \(\boldsymbol{\frac {65} {27} }\)
	E. \(\boldsymbol{\frac {98} {27} }\)