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Mr-mjs-x-3-7-13-27-33-y-find-x-amp-y-any-formula-to-generally-




Question Number 88137 by john santu last updated on 08/Apr/20
Mr mjs   x, 3,7,13,27,33,y  find x & y ? any formula  to generally?
$${Mr}\:{mjs}\: \\ $$$${x},\:\mathrm{3},\mathrm{7},\mathrm{13},\mathrm{27},\mathrm{33},{y} \\ $$$${find}\:{x}\:\&\:{y}\:?\:{any}\:{formula} \\ $$$${to}\:{generally}? \\ $$
Commented by MJS last updated on 08/Apr/20
no  you can look for funny patterns  7−3=4  13−7=6  27−13=14  33−27=6  ⇒  ... 4, 6, 14, 6, 4, 6, 14, 6, 4, 6, 14, 6, ...  ⇒ x=−3∧y=37  or  ... −16, 6, −6, 6, 4, 6, 14, 6, 24, 6, 34, 6, ...  ⇒ x=−3∧y=57    or find a polynome for the given numbers  a_n =−((11)/(12))n^4 +((61)/6)n^3 −((445)/(12))n^2 +((347)/6)n−27  ⇒ x=−27∧y=−7  ...
$$\mathrm{no} \\ $$$$\mathrm{you}\:\mathrm{can}\:\mathrm{look}\:\mathrm{for}\:\mathrm{funny}\:\mathrm{patterns} \\ $$$$\mathrm{7}−\mathrm{3}=\mathrm{4} \\ $$$$\mathrm{13}−\mathrm{7}=\mathrm{6} \\ $$$$\mathrm{27}−\mathrm{13}=\mathrm{14} \\ $$$$\mathrm{33}−\mathrm{27}=\mathrm{6} \\ $$$$\Rightarrow \\ $$$$…\:\mathrm{4},\:\mathrm{6},\:\mathrm{14},\:\mathrm{6},\:\mathrm{4},\:\mathrm{6},\:\mathrm{14},\:\mathrm{6},\:\mathrm{4},\:\mathrm{6},\:\mathrm{14},\:\mathrm{6},\:… \\ $$$$\Rightarrow\:{x}=−\mathrm{3}\wedge{y}=\mathrm{37} \\ $$$$\mathrm{or} \\ $$$$…\:−\mathrm{16},\:\mathrm{6},\:−\mathrm{6},\:\mathrm{6},\:\mathrm{4},\:\mathrm{6},\:\mathrm{14},\:\mathrm{6},\:\mathrm{24},\:\mathrm{6},\:\mathrm{34},\:\mathrm{6},\:… \\ $$$$\Rightarrow\:{x}=−\mathrm{3}\wedge{y}=\mathrm{57} \\ $$$$ \\ $$$$\mathrm{or}\:\mathrm{find}\:\mathrm{a}\:\mathrm{polynome}\:\mathrm{for}\:\mathrm{the}\:\mathrm{given}\:\mathrm{numbers} \\ $$$${a}_{{n}} =−\frac{\mathrm{11}}{\mathrm{12}}{n}^{\mathrm{4}} +\frac{\mathrm{61}}{\mathrm{6}}{n}^{\mathrm{3}} −\frac{\mathrm{445}}{\mathrm{12}}{n}^{\mathrm{2}} +\frac{\mathrm{347}}{\mathrm{6}}{n}−\mathrm{27} \\ $$$$\Rightarrow\:{x}=−\mathrm{27}\wedge{y}=−\mathrm{7} \\ $$$$… \\ $$
Commented by john santu last updated on 08/Apr/20
thank you sir
$${thank}\:{you}\:{sir} \\ $$
Answered by $@ty@m123 last updated on 08/Apr/20
3+10=13  13+20=33  Similarly,  −3+10=7  7+20=27  27+30=57  ∴x=−3  y=57
$$\mathrm{3}+\mathrm{10}=\mathrm{13} \\ $$$$\mathrm{13}+\mathrm{20}=\mathrm{33} \\ $$$${Similarly}, \\ $$$$−\mathrm{3}+\mathrm{10}=\mathrm{7} \\ $$$$\mathrm{7}+\mathrm{20}=\mathrm{27} \\ $$$$\mathrm{27}+\mathrm{30}=\mathrm{57} \\ $$$$\therefore{x}=−\mathrm{3} \\ $$$${y}=\mathrm{57} \\ $$

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