Numbers and Sequences Sequence as a Function A sequence can be considered as a function defined on the set of natural numbers . In particular, a sequence is a function f : ® , where is the set of all real numbers. If the sequence is of the form a a a ,... then we can associate the function to the sequence a a a ,...
by f k a k k = , , ,... Progress Check . Fill in the blanks for the following sequences (i) , , , , ... (ii) , , , , ,… (iii) , , , , , ...
. A sequence is a function defined on the set of . . The n th term of the sequence , , , , ,...
can be expressed as . . Say True or False (i) All sequences are functions (ii) All functions are sequences. Example .
Find the next three terms of the sequences (i) , , , . . . .
. Solution (i) In the above sequence the numerators are same and the denominator is increased by . So the next three terms are a a a (ii) Here each term is decreased by . So the next three terms are - , - , - .
(iii) a a a a a Fig . N f R , , , , ... + + +