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Question-94960




Question Number 94960 by bshahid010@gmail.com last updated on 22/May/20
Answered by Kunal12588 last updated on 22/May/20
2+(n−1)(3)=2+(n_1 −1)(5)  ⇒3n−1=5n_1 −3  ⇒5n_1 −3n=2  n_1 =1+3t  n=1+5t   ((n),(n_1 ) ) =  ((1,6,(11),(16)),(1,4,7,(10)) )  4 common terms
$$\mathrm{2}+\left({n}−\mathrm{1}\right)\left(\mathrm{3}\right)=\mathrm{2}+\left({n}_{\mathrm{1}} −\mathrm{1}\right)\left(\mathrm{5}\right) \\ $$$$\Rightarrow\mathrm{3}{n}−\mathrm{1}=\mathrm{5}{n}_{\mathrm{1}} −\mathrm{3} \\ $$$$\Rightarrow\mathrm{5}{n}_{\mathrm{1}} −\mathrm{3}{n}=\mathrm{2} \\ $$$${n}_{\mathrm{1}} =\mathrm{1}+\mathrm{3}{t} \\ $$$${n}=\mathrm{1}+\mathrm{5}{t} \\ $$$$\begin{pmatrix}{{n}}\\{{n}_{\mathrm{1}} }\end{pmatrix}\:=\:\begin{pmatrix}{\mathrm{1}}&{\mathrm{6}}&{\mathrm{11}}&{\mathrm{16}}\\{\mathrm{1}}&{\mathrm{4}}&{\mathrm{7}}&{\mathrm{10}}\end{pmatrix} \\ $$$$\mathrm{4}\:{common}\:{terms} \\ $$
Answered by mr W last updated on 22/May/20
A_n =2+3n=2+3×5m≤59  B_k =2+5k=2+5×3m≤59  m≤((59−2)/(3×5))=3.8  ⇒0≤m≤3  ⇒4 common terms:  2, 17, 32, 47
$${A}_{{n}} =\mathrm{2}+\mathrm{3}{n}=\mathrm{2}+\mathrm{3}×\mathrm{5}{m}\leqslant\mathrm{59} \\ $$$${B}_{{k}} =\mathrm{2}+\mathrm{5}{k}=\mathrm{2}+\mathrm{5}×\mathrm{3}{m}\leqslant\mathrm{59} \\ $$$${m}\leqslant\frac{\mathrm{59}−\mathrm{2}}{\mathrm{3}×\mathrm{5}}=\mathrm{3}.\mathrm{8} \\ $$$$\Rightarrow\mathrm{0}\leqslant{m}\leqslant\mathrm{3} \\ $$$$\Rightarrow\mathrm{4}\:{common}\:{terms}: \\ $$$$\mathrm{2},\:\mathrm{17},\:\mathrm{32},\:\mathrm{47} \\ $$

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