Patterns, Sequences, and Series

When we add the terms of a sequence together, we form a series. We use the symbol Sn to show the sum of the first n terms of a series. So, Sn = T1+T2+T3+T4+...+Tn   Arithmetic Series The formula is   Where: Sn is the sum of n terms. a is the...

When there is a common ratio (r) between consecutive terms, we can say this is a geometric sequence. If the first term (T1) is a, the common ratio is r, and the general term is Tn, then: Tn= ar n-1 Look at the sequence 5; 15; 45; 135; 405; … Therefore, the...

At least four numbers are needed to determine whether the sequence is quadratic or not. Consider this number pattern: 6; 12; 22; 36; 54. There is no common difference between the numbers. The differences are 6; 10; 14; 18.  Number pattern 6; 12; 22; 36; 54 Now we...

An arithmetic sequence is a sequence where the common difference (d) between consecutive terms is constant. T2-T1 = T4-T3 = Tn-T n-1 =d  (common difference)   Example 2: Given the sequence: 5; 9; 13; 17; … a) Determine the common...

  A list of numbers in order is called a number pattern or number sequence. We need at least three numbers in the list to work out if the numbers form a pattern. If we only have two numbers, we cannot be sure what the pattern is. For example, if we have the list...