# 1, 5, 9, 13, 17....... What is the common difference? 4 Say ‘tn’ represents the nth term. Then ‘tn+1’ represents the next term in the sequence. We can.

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1, 5, 9, 13, 17....... What is the common difference? 4 Say ‘tn’ represents the nth term. Then ‘tn+1’ represents the next term in the sequence. We can re-write the equation as: tn+1 = tn +4 t1 = 1 Or it can be transposed to look like this: tn+1 –tn = 4 t1=1 This is what you call a first order difference eqution.

tn, the previous term tn+1, the next term OR tn-1, the previous term tn, the next term The first term can be represented by either t0 or t1

A starting term is needed to fully define a sequence. The same pattern with different starting points gives different sets of numbers. t n + 1 = t n + 2, t 1 = 3 gives 3, 5, 7, 9, … t n + 1 = t n + 2, t 1 = 2 gives 2, 4, 6, 8,…

 The following equations each define a sequence. Which of them are first order difference equations (defining a relationship between two consecutive terms)?  a t n = t n − 1 + 2 t 1 = 3 n = 1, 2, 3, …  b t n = 4 + 2 n n = 1, 2, 3, …  c f n + 1 = 3 f n n = 1, 2, 3, …

What is the first five terms of the sequence defined by the first order difference equation? t n = 3 t n − 1 + 5 t 0 = 2

A sequence is defined by the first order difference equation: t n + 1 = 2 t n − 3 n = 1, 2, 3, … If the fourth term of the sequence is − 29, that is, t 4 = − 29, then what is the second term?

 EXERCISE 6A pg 263 Q’s 1-10

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