1. 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 …
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