An-AP-has-41-terms-The-sum-of-the-first-five-terms-of-this-AP-is-35-and-the-sum-of-the-last-five-terms-of-the-same-AP-is-395-find-the-common-difference-and-the-first-term-

Question Number 38025 by mondodotto@gmail.com last updated on 20/Jun/18

$$\boldsymbol{\mathrm{An}}\:\boldsymbol{\mathrm{AP}}\:\boldsymbol{\mathrm{has}}\:\mathrm{41}\:\boldsymbol{\mathrm{terms}}.\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{five}} \\ $$$$\boldsymbol{\mathrm{terms}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{AP}}\:\boldsymbol{\mathrm{is}}\:\mathrm{35}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{last}}\:\boldsymbol{\mathrm{five}}\:\boldsymbol{\mathrm{terms}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{same}}\:\boldsymbol{\mathrm{AP}}\:\boldsymbol{\mathrm{is}}\:\mathrm{395}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{common}}\:\boldsymbol{\mathrm{difference}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{first}}\:\boldsymbol{\mathrm{term}}. \\ $$

Answered by ajfour last updated on 20/Jun/18

$$\mathrm{5}{a}+\mathrm{10}{d}=\mathrm{35} \\ $$$$\mathrm{5}{a}+\left(\mathrm{40}+\mathrm{39}+\mathrm{38}+\mathrm{37}\right){d}=\mathrm{395} \\ $$$$\Rightarrow\:\:{d}=\frac{\mathrm{360}}{\mathrm{144}}\:=\:\frac{\mathrm{5}}{\mathrm{2}} \\ $$$${and}\:\:\:{a}=\mathrm{2}\:. \\ $$

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