#1){3*n+1}={4,7,10,13}
[3*n+1 for n in range(1,4)]
[4, 7, 10] [4, 7, 10] |
sum([3*n+1 for n in range(1,4)])
21 21 |
#2){2*n+5}={5,7,9,11,13,15,17}
[2*n+5 for n in range(7)]
[5, 7, 9, 11, 13, 15, 17] [5, 7, 9, 11, 13, 15, 17] |
sum([2*n+5 for n in range(7)])
77 77 |
#3){4-n}={4,3,2,1,0,-1}
[4-n for n in range(6)]
[4, 3, 2, 1, 0, -1] [4, 3, 2, 1, 0, -1] |
sum([4-n for n in range(6)])
9 9 |
(4+(-1))/2*6
9 9 |
#4){2,6,10,...}=?
[4*n+2 for n in range(10)]
[2, 6, 10, 14, 18, 22, 26, 30, 34, 38] [2, 6, 10, 14, 18, 22, 26, 30, 34, 38] |
#4)13th term?
[4*n+2 for n in range(13)]
[2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50] [2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50] |
#4)sum?
(2+50)/2*13
338 338 |
sum([4*n+2 for n in range(13)])
338 338 |
#p829(52) {100,98,96,...}
[-2*n+100 for n in range(30)]
[100, 98, 96, 94, 92, 90, 88, 86, 84, 82, 80, 78, 76, 74, 72, 70, 68, 66, 64, 62, 60, 58, 56, 54, 52, 50, 48, 46, 44, 42] [100, 98, 96, 94, 92, 90, 88, 86, 84, 82, 80, 78, 76, 74, 72, 70, 68, 66, 64, 62, 60, 58, 56, 54, 52, 50, 48, 46, 44, 42] |
(100+42)/2*30
2130 2130 |
sum([-2*n+100 for n in range(30)])
2130 2130 |
#p829(53) sum({10,14,18,22,...,a(n)})=2040, n=?
[4*n+10 for n in range(10)]
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equ=(10+(4*x+10))/2*(x+1)==2040;show(equ)
equ=expand(equ);show(equ)
equ=equ-2040;show(equ)
equ=equ/2;show(equ)
equ=factor(equ);show(equ)
solve(equ,x)
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def root1(a,b,c):
return (-b+sqrt(b^2-4*a*c))/(2*a)
root1(2,12,-2030).n()
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def root2(a,b,c):
return (-b-sqrt(b^2-4*a*c))/(2*a)
root2(2,12,-2030).n()
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plot(equ,-40,30)
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