1202 What is an Arithmetic Sequence?

3012 days ago by MATH4R2012

#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)] 
       
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) 
       





def root1(a,b,c): return (-b+sqrt(b^2-4*a*c))/(2*a) root1(2,12,-2030).n() 
       
def root2(a,b,c): return (-b-sqrt(b^2-4*a*c))/(2*a) root2(2,12,-2030).n() 
       
plot(equ,-40,30)