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-

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

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

Answered by ajfour last updated on 20/Jun/18

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

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