Generating sequences A1.1 Core Plenary Make (generate) some arithmetic sequences of your own using different 1st terms and term-to-term rules. Investigate the difference between the 6th and 3rd terms for each of the sequences you have written. For example First term = 5 Term-to-term rule = + 3 5 8 11 14 17 20 23 … 6th term – 3rd term = 20 – 11 = 9 Preamble This activity allows pupils to experiment with and investigate some arithmetic sequences of their own. There are opportunities to expose the more capable to some elementary proof regarding the difference between certain terms (in the example here, the 6th and the 3rd terms). Possible content Working with and investigating simple arithmetic sequences. Resources None. Solution/Notes The general rule, true for all arithmetic sequences, is that the difference between the 6th and 3rd terms is three times the difference between consecutive terms. This can (for the more capable) be proved using a little algebra. For a sequence with first term a and term-to-term rule add b: a a + b a + 2b a + 3b a + 4b a + 5b … so 6th term − 3rd term = a + 5b − (a + 2b) = 3b Original Material © Cambridge University Press 2009 Original Material © Cambridge University Press 2009