Datele problemei:
[tex]q = 2 cm \\ b1 = 9 cm \\ S_{n} = 279 cm(perimetru)\\ n = ?[/tex](n = numar de laturi ale poligonului)Rezolvare:
Mă folosesc de formulei sumei a n termeni:[tex]S_{n}=b_{1}*\frac{q^n-1}{q-1}[/tex]Stiu ca b1 = 9, q = 2 si Sn = 279. Inlocuind:[tex]279 = 9*\frac{2^n11}{2-1}\\\frac{279}{9}=2^n-1\\31+1 = 2^n\\2^n=32 = > n=log_{2}32 = 5[/tex]Așadar poligonul are 5 laturi.
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Datele problemei:
[tex]q = 2 cm \\ b1 = 9 cm \\ S_{n} = 279 cm(perimetru)\\ n = ?[/tex](n = numar de laturi ale poligonului)
Rezolvare:
Mă folosesc de formulei sumei a n termeni:
[tex]S_{n}=b_{1}*\frac{q^n-1}{q-1}[/tex]
Stiu ca b1 = 9, q = 2 si Sn = 279. Inlocuind:
[tex]279 = 9*\frac{2^n11}{2-1}\\\frac{279}{9}=2^n-1\\31+1 = 2^n\\2^n=32 = > n=log_{2}32 = 5[/tex]
Așadar poligonul are 5 laturi.