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In-an-A-P-the-common-difference-is-2-and-the-largest-term-exceeds-the-middle-term-by-58-Find-the-smallest-term-of-the-A-P-

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Question Number 19683 by 786786AM last updated on 14/Aug/17
In an A.P; the common difference is −2 and the largest term exceeds the middle term by 58. Find the smallest term of the A.P.
$$\mathrm{In}\:\mathrm{an}\:\mathrm{A}.\mathrm{P};\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{is}\:−\mathrm{2}\:\mathrm{and}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{term}\:\:\mathrm{exceeds}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{by}\:\mathrm{58}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{A}.\mathrm{P}. \\ $$
Answered by Rasheed.Sindhi last updated on 15/Aug/17
Let m is a middle term m+58 is the largest term. ∴ m−58 is the smallest term. AP will be: m+58,m+56,...,m,m−2,...,m−58 The smallest term=m−58 m: Middle term
$$\mathrm{Let}\:\mathrm{m}\:\mathrm{is}\:\mathrm{a}\:\mathrm{middle}\:\mathrm{term} \\ $$$$\mathrm{m}+\mathrm{58}\:\mathrm{is}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{term}. \\ $$$$\therefore\:\mathrm{m}−\mathrm{58}\:\mathrm{is}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{term}. \\ $$$$\mathrm{AP}\:\:\mathrm{will}\:\mathrm{be}: \\ $$$$\mathrm{m}+\mathrm{58},\mathrm{m}+\mathrm{56},…,\mathrm{m},\mathrm{m}−\mathrm{2},…,\mathrm{m}−\mathrm{58} \\ $$$$\mathrm{The}\:\mathrm{smallest}\:\mathrm{term}=\mathrm{m}−\mathrm{58} \\ $$$$\:\:\:\:\:\:\:\mathrm{m}:\:\mathrm{Middle}\:\mathrm{term} \\ $$

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