MATH 1019 Lecture Notes - Lecture 12: Savings Account, Points Of The Compass

• School: York University
• Department: Mathematics and Statistics
• Course: MATH 1019
• Professor: Natasha May

Document Summary

Sequences: sequences: ordered list of elements, ex: 1,2,3,5,8, sequence: fu(cid:374)(cid:272)tio(cid:374) f(cid:396)o(cid:373) a su(cid:271)set of the i(cid:374)tege(cid:396)s (cid:894)usually eithe(cid:396) the set{(cid:1004),(cid:1005),(cid:1006),(cid:1007),(cid:1008), } o(cid:396) {(cid:1005),(cid:1006),(cid:1007),(cid:1008), }(cid:895) to a set s: geometric progression, sequence of the form: a, ar, ar2, . ,a(cid:396)n, a: initial term r: common ratio, ex: let a=2 and r=5. {bn} = {b0,b1,b2, } = {(cid:1006),(cid:1005)(cid:1004),(cid:1009)(cid:1004),(cid:1006)(cid:1009)(cid:1004),(cid:1005)(cid:1006)(cid:1009)(cid:1004), : arithmetic progression, se(cid:395)ue(cid:374)(cid:272)e of the fo(cid:396)(cid:373): a,a+d,a+(cid:1006)d, ,a+(cid:374)d, , a: initial number, d: common difference, ex: let a =-1 and d=4. [here a0=2 is the initial condition. ] a1 = a0+3=2+3=5 a2=5+3=8 a3 = 8+3=11: fibonacci sequence, defined by: Iterative solution example: method 1: working upward, forward substitution, a. +3 =(2+3 (n 2))+3=2+3(n 1: financial application, ex: suppose that a person deposits ,000. 00 in a savings account at a bank yielding. How much will be in the account after. 30 years: let pn denote the amount in the account after 30 years.