IB›IB Maths: Analysis and Approaches SL›Mind maps1.2 Arithmetic sequences and seriesIB Maths: Analysis and Approaches SL: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsSequenceAdd the same amount each timeCommon difference d=un+1−und = u_{n+1} - u_nd=un+1−unun=u1+(n−1)du_n = u_1 + (n-1)dun=u1+(n−1)dnnn must be a positive integerSeries sumSn=n2(2u1+(n−1)d)S_n = \frac{n}{2}(2u_1 + (n-1)d)Sn=2n(2u1+(n−1)d)Sn=n2(u1+un)S_n = \frac{n}{2}(u_1 + u_n)Sn=2n(u1+un) if last term knownGiven SnS_nSn, solve a quadratic in nnnReject negative or non-integer nnnSigma notation∑r=1n(7r−2)=5+12+19+…\sum_{r=1}^{n}(7r-2) = 5 + 12 + 19 + \dots∑r=1n(7r−2)=5+12+19+…Coefficient of rrr is the common differenceFirst term: put rrr = lower limitTerms = top − bottom + 1Arithmeticsequences and seriesunu_nunSnS_nSndddApplicationsSimple interest is arithmetic4000 AED at 3.5%: d=140d = 140d=140Compare models with an inequalityNearly arithmetic data: use mean differenceExtrapolation less reliable than interpolationWorked exampleFind ddd if u3=11u_3 = 11u3=11, u8=31u_8 = 31u8=31Subtract: 5d=205d = 205d=20So d=4d = \mathbf{4}d=4Exam tipsUse n−1n-1n−1 differences, not nnnConstant in 7r−27r-27r−2 is not the first termAnswer in context: 34 complete yearsGDC sum: still identify u1u_1u1 and ddd