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Category: Coordinate Geometry

Given-a-sequence-u-n-defined-reculsively-by-u-n-1-3u-n-4u-n-1-u-0-1-u-2-3-show-that-u-n-1-4u-n-1-n-1-3u-0-4u-1-hence-show-that-u-n-is-a-divegent-sequence-

Question Number 127116 by physicstutes last updated on 27/Dec/20 Givenasequence(un)definedreculsivelybyun+1=3un+4un1,u0=1,u2=3$$\:\mathrm{show}\:\mathrm{that}\:\:{u}_{{n}+\mathrm{1}} −\mathrm{4}{u}_{{n}} \:=\:\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \left(\mathrm{3}{u}_{\mathrm{0}} −\mathrm{4}{u}_{\mathrm{1}} \right)…

If-p-x-1-x-2-x-i-and-q-y-1-y-2-y-i-form-two-infinite-arithmetic-sequences-with-common-difference-a-and-b-respectively-then-find-the-locus-of-the-point-where-1-n-

Question Number 61274 by alphaprime last updated on 31/May/19 Ifp,x1,x2,xiandq,y1,y2,yiformtwoinfinitearithmeticsequenceswithcommondifferenceaandbrespectively,thenfindthelocusofthepoint(α,β)$${where}\:\alpha\:=\:\frac{\mathrm{1}}{{n}}\:\sum_{{i}=\mathrm{1}} ^{{n}}…