# my1202 What's an Arithmetic Sequence?

## 3178 days ago by MATH4R2012

#1){3*n+1}={4,7,10,13} [3*n+1 for n in range(1,5)]
 $\newcommand{\Bold}{\mathbf{#1}}\left[4, 7, 10, 13\right]$
sum([3*n+1 for n in range(1,5)])
 $\newcommand{\Bold}{\mathbf{#1}}34$
#2){3*n+5}={5,8,11,14} [3*n+5 for n in range(4)]
 $\newcommand{\Bold}{\mathbf{#1}}\left[5, 8, 11, 14\right]$
sum([3*n+5 for n in range(4)])
 $\newcommand{\Bold}{\mathbf{#1}}38$
#3){4-n}={4,3,2,1,0,-1} [4-n for n in range(6)]
 $\newcommand{\Bold}{\mathbf{#1}}\left[4, 3, 2, 1, 0, -1\right]$
sum([4-n for n in range(6)])
 $\newcommand{\Bold}{\mathbf{#1}}9$
#4){2,6,10,...}=? [4*n-2 for n in range(1,6)]
 $\newcommand{\Bold}{\mathbf{#1}}\left[2, 6, 10, 14, 18\right]$
#4)13th term? [4*n-2 for n in range(1,14)]
 $\newcommand{\Bold}{\mathbf{#1}}\left[2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50\right]$
#4)sum of 13 terms? (2+50)/2*13
 $\newcommand{\Bold}{\mathbf{#1}}338$
#p829(52) {100,98,96,...} [-2*n+102 for n in range(1,10)]
 $\newcommand{\Bold}{\mathbf{#1}}\left[100, 98, 96, 94, 92, 90, 88, 86, 84\right]$
#p829(52) 30th step? [-2*n+102 for n in range(1,31)]
 $\newcommand{\Bold}{\mathbf{#1}}\left[100, 98, 96, 94, 92, 90, 88, 86, 84, 82, 80, 78, 76, 74, 72, 70, 68, 66, 64, 62, 60, 58, 56, 54, 52, 50, 48, 46, 44, 42\right]$
#p829(52) how many bricks? (100+42)/2*30
 $\newcommand{\Bold}{\mathbf{#1}}2130$
#p829(53) {10,14,18,...} [4*n+6 for n in range(1,10)]
 $\newcommand{\Bold}{\mathbf{#1}}\left[10, 14, 18, 22, 26, 30, 34, 38, 42\right]$
#p829(53) how many rows if whole section has 2040 seats? equ=(10+(4*x+6))/2*x==2040;show(equ) equ=expand(equ);show(equ) equ=equ-2040;show(equ) equ=factor(equ);show(equ) solve(equ,x)
 \newcommand{\Bold}{\mathbf{#1}}2 \, {\left(x + 4\right)} x = 2040 \newcommand{\Bold}{\mathbf{#1}}2 \, x^{2} + 8 \, x = 2040 \newcommand{\Bold}{\mathbf{#1}}2 \, x^{2} + 8 \, x - 2040 = 0 \newcommand{\Bold}{\mathbf{#1}}2 \, {\left(x - 30\right)} {\left(x + 34\right)} $\newcommand{\Bold}{\mathbf{#1}}\left[x = \left(-34\right), x = 30\right]$
[4*n+6 for n in range(1,31)]
 $\newcommand{\Bold}{\mathbf{#1}}\left[10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126\right]$
(10+126)/2*30
 $\newcommand{\Bold}{\mathbf{#1}}2040$
plot(2*x^2+8*x-2040,-50,50)  