IGCSE›Edexcel IGCSE Maths›Mind mapsSequencesEdexcel IGCSE Maths: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsRulesA term-to-term rule gets the next term from the lastA position-to-term rule jumps to any termTerm-to-term alone cannot give the 50th term directlyLinear nth termConstant common difference dddun=dn+(a−d)u_n = dn + (a-d)un=dn+(a−d)Coefficient of nnn equals ddd5,8,11,14→3n+25, 8, 11, 14 \rightarrow 3n+25,8,11,14→3n+2QuadraticSecond differences are constantaaa is half the second differenceSubtract an2an^2an2 to leave a linear sequence2,7,14,23→n2+2n−12, 7, 14, 23 \rightarrow n^2+2n-12,7,14,23→n2+2n−1Sequencespatterns of termsunu_nunn2n^2n2Special sequencesSquare: 1, 4, 9, 16, 25Cube: 1, 8, 27, 64Triangular: 1, 3, 6, 10, n(n+1)2\frac{n(n+1)}{2}2n(n+1)Fibonacci-type: add the previous two termsGeometricConstant common ratio rrrun=arn−1u_n = ar^{n-1}un=arn−1Find rrr by dividing consecutive terms3,6,12,243, 6, 12, 243,6,12,24: r=2r = 2r=2Exam tipsForgetting to halve the second differenceNever subtract to find rrrCheck by substituting n=1,2,3n = 1, 2, 3n=1,2,3