Oblicz brakujace wyrazu ciągu arytmetycznego.a) -3,-4 i 1/2, a,b,c,db) a,5,b,c,d,17c) a,b,c,-7,d,-11.... Question from @Lenusia17

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Oblicz brakujace wyrazu ciągu arytmetycznego.a) -3,-4 i 1/2, a,b,c,d
b) a,5,b,c,d,17
c) a,b,c,-7,d,-11
d) a,-5,b,c,-1/2,d

Bardzo proszę pilne! :)

krysta $a)\\\\ -3,\ \ -4 \frac{1}{2},\ a,\ b,\ c,\ d \\ \\mamy\\\\a_{1} = - 3, \ \ a_{2} = - 4\frac{ 1}{2} \\\\zatem\\\\ r = a _{2} - a _{2} = - 4\frac{1}{2} - (-3) = - 4 \frac{1}{2} + 3 = -1 \frac{1}{2} \\ \\a = a_{2} + r = - 4 \frac{1}{2} + ( - 1 \frac{1}{2} ) = - 6$

$b = a + r = - 6 + ( - 1 \frac{1}{2}) = - 7 \frac{1}{2}\\\\c =b+ r = - 7 \frac{1}{2} = ( - 1 \frac{1}{2} ) = - 9\\ \\d = c + r = - 9 + ( - 1 \frac{1}{2}) = - 10 \frac{1}{2}\\ \\-3, \ \ -4\frac{1}{2},\ \ -6, \ \ -7\frac{1}{2}, \ \ -9, \ \ -10\frac{1}{2}$

$b)\\\\ a,5,b,c,d,17 \\\\a_{2} = 5\\\\a_{6} = 17\\\\mamy\\\\a_{2}=a+r \\a_{6}=a+5r$

$zatem \\\\ a_{6}-a_{2}=17-5=12 \\ i \\ a_{6} - a_{2} = (a + 5r ) - ( a + r ) = a + 5r - a - r = 4r\\ \\12=4r\ \ / :4 \\ \\r=3$

$a = a_{2} - r = 5 - 3 = 2\\\\b=a_{2}+r=5+3= 8\\\\c = b + r = 8 + 3 = 11\\\\d = c + r = 11 + 3 = 14 \\\\2, \ \5, \ \ 8, \ \ 11, \ \ 14, \ \ 17$

$c)\\ \\ a,b,c,-7,d,-11 \\\\a_{4}=-7 , \ \ a_{6}=-11\\\\mamy\\\\a_{4}=a+3r , \ \ a_{6}=a+5r \\\\zatem$

$a_{6}-a_{4}=a+5r-(a+3r)=a+5r- a-3r =2r \\\\a_{6}-a_{4}=-11-(-7)=-11+7=-4 \\\\2r =-4 \ \ / :2\\\\r=-2$

$d=a_{4}+r=-7+ (-2)=-9 \\\\c=a_{4}-7=-7-(-2)=-7+2=-5 \\ \\b= c-r=-5-(-2)=-5+2=-3\\\\a=b-r=-3-(-2)=-3+2=-1\\\\-1, \ \ -3, \ \ -5, \ \ -7, \ \ -9, \ \ -11$

$d)\\\\ a,\ \ -5,\ \ b,\ \ c,\ \ - \frac{1}{2},\ \ d\\\\a_{2} = - 5,\ \ \ a_{5}=-\frac{1}{2}\\ \\ mamy: \\\\a_{2}=a+r , \ \ \ a_{5} =a + 4r \\ zatem$

$a_{5}- a_{2} =a + 4r -(a+r)=a + 4r - a-r=3r\\oraz\\a_{5}-a_{2}=-\frac{1}{2}-(-5)=-\frac{1}{2}+5=4\frac{1}{2}\\\\3r = 4 \frac{1}{2}\\\\3r=\frac{9}{2} \ \ / *\frac{1}{3}\\ \\r=\frac{3}{2}=1\frac{1}{2}$

$a = a _{2} - r = -5 - 1 \frac{1}{2} = - 6 \frac{1}{2}\\\\b=a_{2} +r=-5 +1\frac{1}{2}=-3\frac{1}{2}\\\\c=b+r=-3\frac{1}{2}+1\frac{1}{2}=-2 \\\\d=a_{5}+r=-\frac{1}{2}+1\frac{1}{2}=1\\\\-6\frac{1}{2}, \ \ -5, \ \ -3\frac{1}{2}, \ \ 2, \ \ -\frac{1}{2}, 1$

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