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Question Number 56594 by Joel578 last updated on 19/Mar/19

$$\mathrm{Find}\mathrm{the}n\mathrm{th}\mathrm{term}\mathrm{of}\mathrm{the}\mathrm{sequence}$$$$\left(a\right)\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{7}{62},...$$$$\left(b\right)\frac{1}{2},\frac{1}{4},\frac{1}{8},0,...$$

Answered by MJS last updated on 19/Mar/19

$$\mathrm{there}\mathrm{are}\mathrm{always}\mathrm{\infty }\mathrm{possibilities}$$$$\mathrm{with}\mathrm{four}\mathrm{terms}\mathrm{given},\mathrm{we}\mathrm{can}\mathrm{match}\mathrm{with}$$$$x_n=c_3{n}^3+c_2{n}^2+c_{1}n+c_0$$$$(\mathrm{or}\mathrm{any}\mathrm{other}\mathrm{model}\mathrm{with}4\mathrm{independent}$$$$\mathrm{constants})$$$$\mathrm{we}\mathrm{get}$$$$\left(a\right)x_n=-\frac{1}{496}{n}^3+\frac{37}{496}{n}^2-\frac{57}{124}n+\frac{55}{62}$$$$\left(b\right)x_n=-\frac{1}{48}{n}^3+\frac{3}{16}{n}^2-\frac{2}{3}n+1$$

Commented by Joel578 last updated on 19/Mar/19

$$thankyousirMJS$$$$but,whichformuladiduhaveused?$$$$Imean,thechapterthatstudyingthisformula$$

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