Menu Close

Category: Arithmetic

In-the-sequence-1-22-333-10101010101010101010-1111111111111111111111-The-sum-of-the-digits-in-the-200th-term-is-

Question Number 42495 by Tawa1 last updated on 26/Aug/18 $$\mathrm{In}\:\mathrm{the}\:\mathrm{sequence}\:\:\mathrm{1},\:\mathrm{22},\:\mathrm{333},\:…\:\mathrm{10101010101010101010},\:\mathrm{1111111111111111111111},\:… \\ $$$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{in}\:\mathrm{the}\:\mathrm{200th}\:\mathrm{term}\:\mathrm{is}\:?? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

k-1-n-1-1-k-2-1-1-k-2-

Question Number 107974 by Ar Brandon last updated on 13/Aug/20 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{k}\right)^{\mathrm{2}} }} \\ $$ Answered by Dwaipayan Shikari last updated on 14/Aug/20…

When-the-terms-of-a-Geometric-Progression-G-P-with-r-2-is-added-to-the-corresponding-terms-of-an-arithmetic-progression-A-P-a-new-sequence-is-formed-If-the-first-terms-of-the-GP-and-AP-are-the

Question Number 173178 by pete last updated on 07/Jul/22 $$\mathrm{When}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Geometric}\:\mathrm{Progression}\:\left(\mathrm{G}.\mathrm{P}.\right) \\ $$$$\mathrm{with}\:\mathrm{r}=\mathrm{2}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{the}\:\mathrm{corresponding} \\ $$$$\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{progression}\:\left(\mathrm{A}.\mathrm{P}.\right), \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{formed}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{first}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{and}\:\mathrm{AP}\:\mathrm{are}\:\mathrm{the}\:\mathrm{same}\:\mathrm{and}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{three}\:\mathrm{termsof}\:\mathrm{the}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{are} \\ $$$$\mathrm{3},\:\mathrm{7}\:\mathrm{and}\:\mathrm{11}\:\mathrm{respectively},\:\mathrm{find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{sequence} \\…

x-y-y-x-49-48-x-y-7-2-find-x-and-y-k-k-

Question Number 41958 by 123456780 last updated on 15/Aug/18 $$\begin{cases}{\mathrm{x}^{\sqrt{\mathrm{y}}} +\mathrm{y}^{\sqrt{\mathrm{x}}} =\frac{\mathrm{49}}{\mathrm{48}}}\\{\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}=\frac{\mathrm{7}}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\mathrm{k}.\mathrm{k} \\ $$ Answered by MJS last updated on 16/Aug/18…

Question-172999

Question Number 172999 by Mikenice last updated on 04/Jul/22 Answered by MikeH last updated on 05/Jul/22 $$\mathrm{2}{S}\:=\:{n}\left[\mathrm{2}{a}\:+\:{nd}−{d}\right] \\ $$$$\Rightarrow\:\mathrm{2}{S}\:=\:\mathrm{2}{an}\:+\:{n}^{\mathrm{2}} {d}\:−\:{dn} \\ $$$$\Rightarrow\:{n}^{\mathrm{2}} {d}\:+\:\left(\mathrm{2}{a}−{d}\right){n}−\mathrm{2}{S}\:=\:\mathrm{0} \\ $$$${n}\:=\:\frac{\left({d}−\mathrm{2}{a}\right)\pm\sqrt{\left(\mathrm{2}{a}−{d}\right)^{\mathrm{2}}…