Question and Answers Forum

All Questions      Topic List

UNKNOWN Questions

Previous in All Question      Next in All Question      

Previous in UNKNOWN      Next in UNKNOWN      

Question Number 18207 by potata8 last updated on 16/Jul/17

If ((3+5+7+...+n terms)/(5+8+11+...+10 terms)) = 7, then the  value of n is

$$\mathrm{If}\:\frac{\mathrm{3}+\mathrm{5}+\mathrm{7}+...+{n}\:\mathrm{terms}}{\mathrm{5}+\mathrm{8}+\mathrm{11}+...+\mathrm{10}\:\mathrm{terms}}\:=\:\mathrm{7},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{n}\:\mathrm{is} \\ $$

Answered by Tinkutara last updated on 17/Jul/17

3 + 5 + 7 + ... + (n terms) = (n/2)[6 + (n − 1)2]  = (n/2)(2n + 4) = n(n + 2)  5 + 8 + 11 + ... + (10 terms) =  ((10)/2)[10 + 9×3] = 5×37 = 185  ∴ ((n(n + 2))/(185)) = 7  ⇒ n^2  + 2n − 1295 = 0  n = ((−2 ± 72)/2) = −1 ± 36 = 35 or −37  ∴ n = 35.

$$\mathrm{3}\:+\:\mathrm{5}\:+\:\mathrm{7}\:+\:...\:+\:\left({n}\:\mathrm{terms}\right)\:=\:\frac{{n}}{\mathrm{2}}\left[\mathrm{6}\:+\:\left({n}\:−\:\mathrm{1}\right)\mathrm{2}\right] \\ $$$$=\:\frac{{n}}{\mathrm{2}}\left(\mathrm{2}{n}\:+\:\mathrm{4}\right)\:=\:{n}\left({n}\:+\:\mathrm{2}\right) \\ $$$$\mathrm{5}\:+\:\mathrm{8}\:+\:\mathrm{11}\:+\:...\:+\:\left(\mathrm{10}\:\mathrm{terms}\right)\:= \\ $$$$\frac{\mathrm{10}}{\mathrm{2}}\left[\mathrm{10}\:+\:\mathrm{9}×\mathrm{3}\right]\:=\:\mathrm{5}×\mathrm{37}\:=\:\mathrm{185} \\ $$$$\therefore\:\frac{{n}\left({n}\:+\:\mathrm{2}\right)}{\mathrm{185}}\:=\:\mathrm{7} \\ $$$$\Rightarrow\:{n}^{\mathrm{2}} \:+\:\mathrm{2}{n}\:−\:\mathrm{1295}\:=\:\mathrm{0} \\ $$$${n}\:=\:\frac{−\mathrm{2}\:\pm\:\mathrm{72}}{\mathrm{2}}\:=\:−\mathrm{1}\:\pm\:\mathrm{36}\:=\:\mathrm{35}\:\mathrm{or}\:−\mathrm{37} \\ $$$$\therefore\:\boldsymbol{{n}}\:=\:\mathrm{35}. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com