The first term of an arithmetic progression is $100$ and the common difference is $-5$. The answer should be $20$, but how? Please explain the solution.
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1Is there any relation between your $;n;$ and your $;m;$, or perhaps there's a typo there? – DonAntonio Apr 17 '16 at 05:05
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Sorry it was a typo.Please continue – Saud Kamran Apr 17 '16 at 08:30
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The equality of sums tells you what the $m+1$'st term ought to be, and from there you can work out what $m$ gives that term. – hardmath Apr 17 '16 at 12:54
2 Answers
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Solve using the formula for the sum of an arithmetic progression
$$S_m:=\frac m2\left(200-5(m-1)\right)=\frac{m+1}2\left(200-5m\right)=S_{m+1}\iff$$
$$205m-5m^2=195m-5m^2+200\iff10m=200$$
DonAntonio
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We are told that $s_{m+1}=s_m$, hence $a_{m+1}=0$. But we also have $a_{m+1}=100-m\cdot5\,$. The conclusion is that $m=20$.
Christian Blatter
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