1202 What's an Arithmetic Sequence?

2641 days ago by MATH4R2013

#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)) 
       
#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)) 
       



#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)) 
       



#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) 
       


#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)])) 
       



#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()) 
       








#30 rows!!! factor(equ) solve(equ,x) 
       
[x == -35, x == 29]
[x == -35, x == 29]