- Every Sunday Graham jogs 3 miles. For the rest of the week, each day he jogs 1 mile more than the preceding day. How many miles does Greg jog in 2 weeks?
(A) 42;
(B) 63;
(C) 84;
(D) 98;
(E) 117.
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2I don't really jog, sorry. – gregkow Feb 15 '14 at 18:32
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@gregkow haha, let me edit the question. It now says Graham. – Lost1 Feb 15 '14 at 18:48
2 Answers
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The sum of a finite arithmetic sequence is the average of the first and the last term, times the number of terms. In this case we have (for each week) a seven-term arithmetic sequence where the first term is $3$ and the last term is $9$ (since each day he jogs one more mile, so on the following Saturday, six days later, he will jog $9$ miles). Thus the number of miles jogged per week is $\frac{3+9}{2}\cdot 7=42$. The total number of miles jogged in $2$ weeks is then $2\cdot 42 = 84$.
It's also easy enough to calculate $2\cdot (3+4+5+6+7+8+9)=84$ directly.
ajd
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Given that the week starts on the Sunday, he jogs for $3$, then he jogs for $4,5,6,7,8,9$. Sum these up, you get $42$. Multiplied by $2$ weeks, we get $84$.
Inquest
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