General term

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1. Finding General Term of a Sequence

2. Example 1 . Find the general term of the sequence 2, 4, 6, 8, … Solution Observe the following. 2 = 2(1) – means 1 st term 4 = 2(2) - 2 nd term 6 = 2(3) - 3 rd term 8 = 2(4) - 4 th term The pattern is 2n where n = or n is the position of each term in a sequence. So, the general term of the sequence is f(n) = 2n .  

3. Example 2 . Find the general term of the sequence 1, 3, 5, 7, … Solution Observe the following. 1 = 2(1) – 1 3 = 2(2) – 1 5 = 2(3) – 1 7 = 2(4) – 1 The pattern is 2n – 1 where n = {1, 2, 3, 4, …}. So, the general term of the sequence is f(n) = 2n – 1 .  

4. Example 3 . Find the general term of the sequence 2, 4, 8, 16, … Solution We can express in this manner: 2 = 2 1 4 = 2 2 8 = 2 3 16 = 2 4 The pattern is is 2 n where n = {1, 2, 3, 4, …}. So, the general term of the sequence is f(n) = 2 n .  

5. Example 4 . Find the general term of the sequence 1, 4, 9, 16, … Solution We can be express each term in the following manner: 1 = (1) 2 4 = (2) 2 9 = (3) 2 16 = (4) 2 The pattern is n 2 where n = {1, 2, 3, 4, …}. So, the general term of the sequence is f(n) = n 2 . ;  

6. Theres no definite way or rule in finding the nth term of a given sequences. The following are helpful guide. 1. Find out if there is a common difference between two terms of the given sequence of numbers. 2. Find out if there is a common factor among the terms of the given sequences of numbers. 3. Find out if the given sequence is expressible in exponential form with a common base.