Practise the method.Example 1A pattern has rule T(n)=an2+b, where a and b are constant. Stages 1,2 and 3 contain 3,9 and 19 tiles. How many tiles are at stage 10?Show worked answerAnswer: 201The second difference is 4a=2.Stage 1 gives b=1.Then T(10)=2×102+1=201.Example 2Stage n contains n2+6n+4 tiles. Which positive whole-number stage contains 76 tiles?Show worked answerAnswer: 6Rearrange to n2+6n−72=0=(n−6)(n+12).The positive stage is 6.Example 3A pattern has rule T(n)=an2+b, where a and b are constant. Stages 1,2 and 3 contain 7,25 and 55 tiles. How many tiles are at stage 8?Show worked answerAnswer: 385The second difference is 12a=6.Stage 1 gives b=1.Then T(8)=6×82+1=385.