IB›IB Maths: Analysis and Approaches HL›Mind maps1.2 Arithmetic sequences and seriesIB Maths: Analysis and Approaches HL: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsWhat is it?Add the same amount each timeCommon difference d=un+1−und = u_{n+1} - u_nd=un+1−unTwo terms given → subtract to find dnth termun=u1+(n−1)du_n = u_1 + (n-1)dun=u1+(n−1)dOnly n − 1 differences added18,21,2418, 21, 2418,21,24: u25=90u_{25} = 90u25=90nnn must be a positive integerSum of termsSn=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 → quadratic in nReject negative or non-integer rootsArithmeticsequences and seriesunu_nunSnS_nSndddSigma notation∑r=1n(7r−2)\sum_{r=1}^{n}(7r-2)∑r=1n(7r−2) means add every termCoefficient of rrr is dFirst term: put rrr = lower limitTerms = top − bottom + 1ApplicationsSimple interest gives arithmetic growthCompare models with an inequalityNearly arithmetic data → mean differenceExtrapolation is less reliableExam tipsNot u1+ndu_1 + ndu1+nd for the nth termIn 7r−27r - 27r−2 the first term is 5, not −2Answer in context: after 34 complete years