Sequences, Series and Sigma notation Sequences If you have a set of numbers T1, T2, T3,... where there is a rule for working out the next numbers, we call this set a sequence. Every number in the sequence is called a term and Tn is the nth term. Examples: b) 3, 9, 27, 81... nth term = 3na) 3, 6, 9, 12... nth term = 3n c) 1, 3, 6, 10... nth term = ½ n(n+1) (the triangle numbers)SeriesA series is just when the terms of a sequence are added: T1 + T2 + T3 ... Tn For example: 1 + 2 + 4 + 8 + ... A finite series stops after a certain number of terms, For example: 1 + 3 + 9 + 27 + 81, which has five terms. An infinite series does not stop, Sigma notationWe use the symbol ∑ to define 'the sum of the terms' so that: is the sum of all the terms where t takes the values between 2 and 6 inclusive. Written out in full, this is: Another example: The first term is when t = 3 i. e. 2 × 3 − 6 = 0. The last tern is when t = 12 i. e. 2 × 12 − 6 = 18.