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Definition: A sequence is an ordered set of terms
obtained using a well defined rule. A sequence is written as: ![]() Notes (i) A sequence which goes on forever is called an infinite sequence. A sequence which stops is called a finite sequence. (ii) ![]() ![]() Example 1In the sequence![]() ![]() ![]() (iii) The General term ![]() If you know the general term of a sequence you can work out any other term. Example 2If the general term of a sequence is given by![]() Find ![]() Solution (iv) ![]() Example 3If![]() ![]() Solution (a) The Sum of the first n terms ![]() Students often get un and ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() Example 4For the sequence:![]() ![]() Solution (b) Relationship between ![]() ![]() ![]() Notes: (i) This is a very important result as it is true for all sequences. (ii) Given ![]() ![]() (iii) In a later article we will see how to get ![]() ![]() Example 5If![]() ![]() Solution Example 6If![]() ![]() Show that ![]() Solution Example 7If![]() ![]() Solution Example 8If![]() ![]() Solution |
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