Presentation on theme: "EX 6B THE RELATIONSHIP BETWEEN ARITHMETIC SEQUENCES AND FIRST ORDER DIFFERENCE EQUATIONS."— Presentation transcript:
EX 6B THE RELATIONSHIP BETWEEN ARITHMETIC SEQUENCES AND FIRST ORDER DIFFERENCE EQUATIONS
What defines the ‘first order difference equation’? You will need 3 essential components: 1. A term = tn or tn+1 2. The previous term = tn-1 or tn 3. The starting term = t0 or t1
We can write the equation in two ways tn+1 = tn +3t1 = 3 OR tn = tn-1 + 3t1 = 3 They mean exactly the same thing. Where a term equals to the previous term plus 3.
Pronumeral Conventions TermArithmetic/GeometricFirst Order difference equation First termA or t1T0 or t1 Common differencedb Common ratiora
The ‘common difference’ The common difference, b = t2-t1 = t3-t2 = t5-t4 An arithmetic sequence with a common difference of b may be defined by a first order difference equation of the form: tn+1 = tn + b (or tn+1 – tn = b) Where b is the common difference and for : b>0 it is an increasing sequence b<0 it is a decreasing sequence
Let’s do Questions on pg 267 Lets do question 1, 2, 3, 4 together.