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Category: Arithmetic

if-the-sum-of-first-5-terms-of-a-G-P-is-155-sum-of-last-5-terms-is-39680-first-term-is-5-and-last-term-is-20480-find-the-number-of-terms-of-the-sequence-

Question Number 29645 by gyugfeet last updated on 11/Feb/18 $${if}\:{the}\:{sum}\:{of}\:{first}\:\mathrm{5}\:{terms}\:{of}\:\:{a}\:{G}.{P}.\:{is}\:\mathrm{155},\:{sum}\:{of}\:{last}\:\mathrm{5}\:{terms}\:{is}\:\mathrm{39680},{first}\:{term}\:{is}\:\mathrm{5}\:{and}\:{last}\:{term}\:\:{is}\:\mathrm{20480}.\:{find}\:{the}\:{number}\:{of}\:{terms}\:{of}\:{the}\:{sequence}. \\ $$ Answered by Rasheed.Sindhi last updated on 11/Feb/18 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{is}\:\mathrm{r} \\ $$$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{five}\:\mathrm{terms}: \\ $$$$\mathrm{5}+\mathrm{5r}+\mathrm{5r}^{\mathrm{2}} +\mathrm{5r}^{\mathrm{3}}…

Question-160350

Question Number 160350 by Lekhraj last updated on 28/Nov/21 Answered by Rasheed.Sindhi last updated on 28/Nov/21 $$\mathrm{2001}\:\:\:\:\:{Let}\:{ages}\:{were}\:{x}\:\&\:\mathrm{11}{x} \\ $$$$\mathrm{2018}\:\:\:\:\:\:{x}+\mathrm{17}:\mathrm{11}{x}+\mathrm{17}=\mathrm{2}:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}\left({x}+\mathrm{17}\right)=\mathrm{2}\left(\mathrm{11}{x}+\mathrm{17}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}{x}+\mathrm{85}=\mathrm{22}{x}+\mathrm{34} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{17}{x}=\mathrm{51}\Rightarrow{x}=\mathrm{3}…