Question Number 113374 by Aina Samuel Temidayo last updated on 12/Sep/20
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{next}\:\mathrm{term}\:\mathrm{in}\:\mathrm{this} \\ $$$$\mathrm{sequence}:\:\mathrm{26},\mathrm{63},\mathrm{124},\:\_\_ \\ $$
Commented by Tony6400 last updated on 13/Sep/20
Ans is 209
Commented by Aina Samuel Temidayo last updated on 13/Sep/20
$$\mathrm{Solution}\:\mathrm{please}? \\ $$
Commented by Tony6400 last updated on 13/Sep/20
I have the solution but dont know how to send. Help me
Commented by Tony6400 last updated on 13/Sep/20
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Commented by nimnim last updated on 13/Sep/20
$$\:\:\:\:\:\:\:\mathrm{26},\mathrm{63},\mathrm{124},..... \\ $$$$=\:\left(\mathrm{3}^{\mathrm{3}} −\mathrm{1}\right),\:\left(\mathrm{4}^{\mathrm{3}} −\mathrm{1}\right),\left(\mathrm{5}^{\mathrm{3}} −\mathrm{1}\right),\left(\mathrm{6}^{\mathrm{3}} −\mathrm{1}\right),.... \\ $$$$\therefore\:\mathrm{next}\:\mathrm{term}=\mathrm{6}^{\mathrm{3}} −\mathrm{1}=\mathrm{215} \\ $$
Answered by Tony6400 last updated on 13/Sep/20
Commented by Aina Samuel Temidayo last updated on 13/Sep/20
$$\mathrm{How}\:\mathrm{did}\:\mathrm{you}\:\mathrm{know}\:\mathrm{U}_{\mathrm{n}} =\mathrm{an}^{\mathrm{2}} +\mathrm{bn}+\mathrm{c} \\ $$
Commented by 1549442205PVT last updated on 13/Sep/20
$$\mathrm{This}\:\mathrm{thing}\:\mathrm{depende}\:\mathrm{on}\:\mathrm{view}\:\mathrm{point}\:\mathrm{of} \\ $$$$\mathrm{person}\:\mathrm{who}\:\mathrm{give}\:\mathrm{the}\:\mathrm{question}\:\mathrm{because} \\ $$$$\mathrm{can}\:\mathrm{find}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{3}\: \\ $$$$\mathrm{satisfying}\:\mathrm{U}_{\mathrm{1}} =\mathrm{26},\mathrm{U}_{\mathrm{2}} =\mathrm{63},\mathrm{U}_{\mathrm{3}} =\mathrm{124} \\ $$$$\mathrm{Ex}:\mathrm{U}_{\mathrm{n}} =\mathrm{n}^{\mathrm{3}} +\mathrm{6n}^{\mathrm{2}} +\mathrm{12n}+\mathrm{7} \\ $$