#1) {3n+1}={4,7,10,13,...}
a(n)=3*n+1
print([a(n) for n in range(0,5)])
print(sum([a(n) for n in range(0,5)]))
print((1+13)/2*5)
[1, 4, 7, 10, 13] 35 35 [1, 4, 7, 10, 13] 35 35 |
N=range(0,5)
A=[a(n) for n in range(0,5)]
AN=zip(N,A)
plot(point(AN))
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#2) {2n+5}={5,7,9,11,13,...}
b(n)=2*n+5
show([b(n) for n in range(0,5)])
show(sum([b(n) for n in range(0,5)]))
show((5+13)/2*5)
N=range(5)
B=[b(n) for n in range(0,5)]
BN=zip(N,B)
plot(point(BN))
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#3){4-n}={4,3,2,...}
c(n)=4-n
show([c(n) for n in range(10)])
show(sum([c(n) for n in range(10)]))
show((4-5)/2*10)
N=range(10)
C=[c(n) for n in range(10)]
CN=zip(N,C)
plot(point(CN))
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#4) {d(n)}={2,6,10,14,18,...}
#4) what's the rule?
#4) what's the 13th term?
#4) what's the sum of all 13 terms?
d(n)=4*n+2
show([d(n) for n in range(5)])
show(d(12))
show(sum([d(n) for n in range(13)]))
show((2+50)/2*13)
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#52) p829: {100,98,96,...,?}
#52) p829: each term is the number of bricks on one step of a staircase
#52) p829: if there's 100 bricks in the first step, how many in the 30th step?
#52) p829: if there's 30 steps, how many bricks do you need to build this staircase?
f(n)=-2*n+100
show(f(29))
show((100+42)/2*30)
show([f(n) for n in range(30)])
show(sum([f(n) for n in range(30)]))
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#53) p829: {10,14,18,...,g(n)}
#53) p829: find g(n) the rulle for this arithmetic sequence
#53) p829: each term is the number of seats in a row at the stadium
#53) p829: how many rows are there?
g(n)=4*n+10
show(g(n))
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)
l=solve(equ,x)
show(l)
show(l[1])
show(l[1].rhs())
show(l[1].rhs().n())
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#30 rows!!!
factor(equ)
solve(equ,x)
[x == -35, x == 29] [x == -35, x == 29] |
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