Sequence is the set of terms, usually numbers which follow a certain order or a rule. Here term is each element or number of the sequences. Every sequence can have its own set of rules which it follows. To find the missing terms or following numbers of a sequence the pattern behind the sequence needs to be identified. Some of the very well-known sequences are the arithmetic sequence, geometric sequence, Fibonacci sequence or the triangular sequence. For example in an arithmetic sequence there is a fixed difference between every two consecutive terms. In a geometric sequence there is a fixed ratio which is maintained between two consecutive terms.
Example 1: Find the 15th term in the given sequence 5, 7, 9, 11, 13…..?
Solution: Given in the question is a sequence 5, 7, 9, 11, 13…
The numbers have a fixed difference of 2 i.e 7-5= 9–7= 2.
The 15th term of the sequence can be found by the formula a + (n-1) d
Here a = 5, n = 15 and d = 2.
This gives 5 + (14)* 2 = 33
Hence the 15th term is 33.
Example 2: Find the 11th term in the given sequence 6, 10, 14, 18…..?
Solution: Given in the question is a sequence 6, 10, 14, 18…
The numbers have a fixed difference of 4 i.e 10 - 6 = 4.
The 11th term of the sequence can be found by the formula a + (n-1) d
Here a = 6, n = 11 and d = 4.
This gives 6 + (10)* 4 = 46
Hence the 11th term is 46.