Here are two number sequences. 7 3 4 1 3 2 … 5 30 25 5 20 15 … A1.1 Core Plenary Here are two number sequences. 7 3 4 1 3 2 … 5 30 25 5 20 15 … What is the single rule for generating each of the two sequences? Investigate with some different starting numbers. Jot down anything interesting you find to tell the rest of the class. Preamble In addition to working cooperatively to find the rule, this activity will give pupils the chance to investigate the effects of different starting numbers on sequences and to present their findings. Allow the groups to struggle over finding the rule and encourage discussion and testing. Possible content Finding term-to-term rules, being systematic, practising oral skills. Resources None. Solutions/Notes Each term is the difference between the previous two terms. It appears that terms of this sequence always tend to oscillate, but this may only be after a large number of terms. For example, starting with 1, 17, … the sequence repeats giving … 1, 0, 1, 0, … after twenty-five terms.