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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 byMJS 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 byjohn 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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