boze pomocy nie potrafie zrobic tego prostego zadania, wiem jak ale mi nie wychodzi: Wyznacz liczby: x1, x2, x3, x3, ktore zaznaczono na osi liczbowej(odleglosci miedzy punktami sa jednakowe) a)1/4>>>x1>>>x2>>>x3>>>x4>>>1/3 b)1/5>>>x1>>>x2>>>x3>>>1/4>>>x4

Jezeli dodajemy taka sama liczbe r, to kolejne wyrazy sa yrazami ciagu arytmertycznego. a) 5r = 1/3-1/4 = 4/12 - 3/12 5r=1/12  /:5 r=1/60 x₁=1/4+1/60=15/60+1/60=16/60=4/15 x₂=4/15+1/60=16/60+1/60=17/60 x₃=17/60+1/60=18/60=3/10 x₄=3/10+1/60=18/60+1/60=19/60 b) 4r = 1/4-1/5=1/20  /:4 r=1/80=0,0125 x₁=0,2+0,0125 = 0,2125 x₂=0,2125+0,0125=0,225 x₃=2,375 x₄=0,25+0,0125=0,2625

[latex]a)\a_1 = frac{1}{4}\\a_6 = a_1 + 5r\\frac{1}{3}=frac{1}{4}+5r\\5r = frac{1}{3}-frac{1}{4} = frac{4}{12}-frac{3}{12}\\5r = frac{1}{12} |cdotfrac{1}{5}\\r = frac{1}{60} [/latex] [latex]x_1 = frac{1}{4}+frac{1}{60} = frac{15}{60}+frac{1}{60} = frac{16}{60}\\x_2 = frac{16}{60} + frac{1}{60} = frac{17}{60}\\x_3 = frac{17}{60}+frac{1}{60} =frac{18}{60}\\x_4 = frac{18}{60}+frac{1}{60} = frac{19}{60}[/latex] [latex]b)\a_1 = frac{1}{5}\\a_5 = a_1 + 4r\\frac{1}{4} = frac{1}{5} + 4r\\4r = frac{1}{4}-frac{1}{5} = frac{5}{20}-frac{4}{20}\\4r = frac{1}{20} |cdotfrac{1}{4}\\r = frac{1}{80}[/latex] [latex]x_1 = frac{1}{5}+frac{1}{80} = frac{16}{80}+frac{1}{80} = frac{17}{80}\\x_2 = frac{17}{80} + frac{1}{80} = frac{18}{80}\\x_3 = frac{18}{80} + frac{1}{80} = frac{19}{80}\\x_4 = frac{1}{4}+frac{1}{80} =frac{20}{80}+frac{1}{80} = frac{21}{80}[/latex]