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a) a2 = - 7
a8 = 11
a8 = a1 + 7 r
a2 = a1 + r
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a8 - a2 = (a1 +7r) -(a1 +r) = 6r , ale a8 - a2 = 11 -(-7) = 11+7 = 18
zatem 6r = 18 ---> r = 18 :6 = 3
r = 3
a2 = a1 + r ---> a1 = a2 - r = -7 - 3 = -10
Odp. a1 = -10 oraz r = 3
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z.2
b) -x , 3x +1, -6-x - kolejne wyrazy ciągu arytmetycznego,
zatem
(3x + 1) - (-x) = (-6 - x) - (3x +1)
3x + 1 +x = -6 - x - 3x - 1
4x +1 = -4x -7
4x + 4x = - 7 - 1
8x = -8
x = -8 :8 = -1
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spr.
- (-1) = 1
3*(-1) + 1 = -3 + 1 = -2
-6 -(-1) = -6 +1 = -5
1, -2, -5 - ciąg arytmetyczny o różnicy r = -3
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z.3
a) an = [5n -1 ]/2
an+1 = [5*(n+1) - 1]/2 = [ 5n +5 -1]/2 = [5n +4]/2
r = an+1 - an = [5n +4]/2 - [5n - 1]/2 = [5n +4 - 5n +1]/2 =
= 5/2 = 2.5 > 0
Odp. Różnica ciągu (an) jest równa 2,5.
Ciąg jest rosnący, bo r = 2,5 > 0.
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