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Sequences Revision Wednesday, 24 May 2017 Position to term rules It is important to be able to find the number in a sequence from its position in that sequence. Example. If we want to find the 100th term in the sequence 2, 6, 10, 14,18……… Do we need to keep adding 4, until we find the 100th number in the sequence!! Any suggestions? 1, 2, 3, 4, 5 ……………….Position in sequence (n) 2, 6, 10, 14, 18 ………………. Common difference = 4 4, 8, 12, 16, 20………………. Numbers in 4 x table (4n) To find numbers in sequence multiply position by 4 and take 2 nth Term = 4n – 2 100th term = (4 x 100) – 2 = 398 1, 2, 3, 4, 5 ……………….Position in sequence (n) 8, 13, 18, 23, 28 ………………. Common difference = 5 5, 10, 15, 20, 25………………. Numbers in 5 x table (5n) To find numbers in sequence multiply position by 5 and add 3 nth Term = 5n + 3 100th term = (5 x 100) + 3 = 503 Example Here is a sequence made from match sticks. 𝟔 Diagram 1 𝟏𝟏 𝟏𝟔 Diagram 2 Diagram 3 𝟐𝟏 (a) Draw the next diagram in the sequence. (b) Write down the number of sticks used in each of the first four diagrams. 𝟐𝟏 (c) Write down a formula connecting the number of sticks used and the diagram number. 𝟓𝒏 + 𝟏