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Let-consider-the-following-sequence-1-3-17-5-33-41-What-may-be-the-explicit-formula-that-can-gives-this-sequence-of-number-Thank-you-




Question Number 56426 by Hassen_Timol last updated on 16/Mar/19
Let consider the following sequence :    1 , 3 , (√(17)) , 5 , (√(33)) , (√(41)) , ...     What may be the explicit formula that  can gives this sequence of number ?    Thank you
$${Let}\:{consider}\:{the}\:{following}\:{sequence}\:: \\ $$$$ \\ $$$$\mathrm{1}\:,\:\mathrm{3}\:,\:\sqrt{\mathrm{17}}\:,\:\mathrm{5}\:,\:\sqrt{\mathrm{33}}\:,\:\sqrt{\mathrm{41}}\:,\:…\: \\ $$$$ \\ $$$${What}\:{may}\:{be}\:{the}\:{explicit}\:{formula}\:{that} \\ $$$${can}\:{gives}\:{this}\:{sequence}\:{of}\:{number}\:? \\ $$$$ \\ $$$${Thank}\:{you} \\ $$
Answered by kaivan.ahmadi last updated on 16/Mar/19
(√1),(√9),(√(17)),(√(25)),(√(33)),(√(41)),...  b=1,d=8  b_n =a+(n−1)d=1+(n−1)8=8n−7  a_n =(√(8n−7))
$$\sqrt{\mathrm{1}},\sqrt{\mathrm{9}},\sqrt{\mathrm{17}},\sqrt{\mathrm{25}},\sqrt{\mathrm{33}},\sqrt{\mathrm{41}},… \\ $$$${b}=\mathrm{1},{d}=\mathrm{8} \\ $$$${b}_{{n}} ={a}+\left({n}−\mathrm{1}\right){d}=\mathrm{1}+\left({n}−\mathrm{1}\right)\mathrm{8}=\mathrm{8}{n}−\mathrm{7} \\ $$$${a}_{{n}} =\sqrt{\mathrm{8}{n}−\mathrm{7}} \\ $$$$ \\ $$
Commented by Hassen_Timol last updated on 16/Mar/19
Thank you, I didn′t think about this method...
$${Thank}\:{you},\:{I}\:{didn}'{t}\:{think}\:{about}\:{this}\:{method}… \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 16/Mar/19
(√1) ,(√9) ,(√(17)) ,(√(25)) ,(√(33)) ′(√(41)) ..  T_n =(√(1+(n−1)8)) →(√(8n−7))
$$\sqrt{\mathrm{1}}\:,\sqrt{\mathrm{9}}\:,\sqrt{\mathrm{17}}\:,\sqrt{\mathrm{25}}\:,\sqrt{\mathrm{33}}\:'\sqrt{\mathrm{41}}\:.. \\ $$$${T}_{{n}} =\sqrt{\mathrm{1}+\left({n}−\mathrm{1}\right)\mathrm{8}}\:\rightarrow\sqrt{\mathrm{8}{n}−\mathrm{7}}\: \\ $$

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