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Question Number 109858 by aurpeyz last updated on 26/Aug/20

$$\mathrm{Find}\mathrm{the}\mathrm{nth}\mathrm{term}\mathrm{for}\mathrm{the}\mathrm{sequence}3.12.27.48.75...$$

Answered by Her_Majesty last updated on 26/Aug/20

$$3n^2$$

Answered by 1549442205PVT last updated on 26/Aug/20

$$\mathrm{Since}\mathrm{the}\mathrm{Difference}\mathrm{of}\mathrm{degree}2\mathrm{is}$$$$\mathrm{constant},\mathrm{the}\mathrm{general}\mathrm{terms}\mathrm{has}\mathrm{the}$$$$\mathrm{form}{\mathrm{u}}_{\mathrm{n}}={\mathrm{an}}^2+\mathrm{bn}+\mathrm{c}.\mathrm{Give}\mathrm{n}\mathrm{the}$$$$\mathrm{values}1,2,3...$$

Commented by aurpeyz last updated on 26/Aug/20

$$\mathrm{Pls}\mathrm{what}\mathrm{do}\mathrm{you}\mathrm{mean}\mathrm{give}\mathrm{n}\mathrm{the}\mathrm{value}123?$$$$\mathrm{how}\mathrm{will}\mathrm{that}\mathrm{give}\mathrm{us}\mathrm{the}\mathrm{answer}$$

Commented by 1549442205PVT last updated on 28/Aug/20

$$\mathrm{n}=1\Rightarrow \mathrm{a}.1^2+\mathrm{b}.1+\mathrm{c}=3,\mathrm{n}=2\Rightarrow \mathrm{a}.2^2+\mathrm{b}.2+\mathrm{c}=12$$$$\mathrm{n}=3\Rightarrow \mathrm{a}.3^2+\mathrm{b}.3+\mathrm{c}=27.\mathrm{We}\mathrm{obtain}\mathrm{a}$$$$\mathrm{system}\mathrm{of}\mathrm{three}\mathrm{eqs}.\mathrm{of}\mathrm{degree}1\mathrm{for}3$$$$\mathrm{unknowns}\mathrm{a},\mathrm{b},\mathrm{c}.\mathrm{Solve}\mathrm{this}\mathrm{system}$$

Answered by bemath last updated on 26/Aug/20

$$3;12;27;48;75;...$$$$9;15;21;27$$$$6;6;6;$$$$U_n=3+(n-1).9+\frac{(n-1)(n-2)}{2!}.6$$$$U_n=9n-6+3(n^2-3n+2)$$$$U_n=3n^2+9n-9n-6+6=3n^2$$

Commented by Ari last updated on 26/Aug/20

Dear can you explain to me more clearly how you came to the general formula Un

Commented by aurpeyz last updated on 26/Aug/20

$$\mathrm{I}\mathrm{will}\mathrm{also}\mathrm{like}\mathrm{to}\mathrm{know}\mathrm{please}.$$

Commented by aurpeyz last updated on 26/Aug/20

$$\mathrm{I}\mathrm{will}\mathrm{also}\mathrm{like}\mathrm{to}\mathrm{know}\mathrm{if}\mathrm{i}\mathrm{can}\mathrm{use}\mathrm{this}\mathrm{approach}$$$$\mathrm{for}\mathrm{any}\mathrm{kind}\mathrm{of}\mathrm{question}?$$

Commented by aurpeyz last updated on 27/Aug/20

$$itbistheformulaisNewtonForwardDiffrenceFormula$$

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