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EX 6B

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.

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EX 6B

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  1. EX 6B THE RELATIONSHIP BETWEEN ARITHMETIC SEQUENCES AND FIRST ORDER DIFFERENCE EQUATIONS

  2. 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

  3. We can write the equation in two ways • tn+1 = tn +3 t1 = 3 • OR • tn = tn-1 + 3 t1 = 3 • They mean exactly the same thing. • Where a term equals to the previous term plus 3.

  4. Pronumeral Conventions

  5. 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

  6. Let’s do Questions on pg 267 • Lets do question 1, 2, 3, 4 together.

  7. CLASSWORK/HOMEWORK • EX 6B pg 267 Q’s 1-5

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