A sequence can be defined by its nth term. For the sequence 7,12,17,22,27, Un= 5n+2 because difference of 5 between each term then to get from 5 to 7 you have to add 2.

Recurrance relation

- ak just means the Kth term of the sequence.
- Example find the recurrence relation of the sequences 5,8,11,14,17... The common difference is 3, ak+1=ak+3, so if k=5 then ak=a5 with ak+1=a6 but the description needs to be more specific, you have got to give the first term in the sequence as well as the recurrents relation. Answer: ak+1=ak+3 when a1=5
- Example 2, A sequence is defined by ak+1=2ak-1, a2=5. List the first 5 terms. a3=2x5-1=9, a4=17, a5=33, a1= a2=2a1-1, 5=2a1-1, 6=2a1, 3=a1 therefore the first 5 terms are 3,5,9,17,33.

Types of Sequences

- E.g.ak+1=ak+3 a1=1, 1<k<20 will contain 20 terms meaning it is an finite sequence.
- An infinite sequence wont have a final turm
- Others revisit the same numbers over and over in a period, called a periodic sequence.

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