For a fund-raiser, Anthony earns 5 dollars for the first mile he runs, an additional 7 dollars for the second mile, an additional 9 dollars for the third mile, and so on. The expression the sum from n is equal to 1 to 10 of open bracket 5 plus 2 close bracket represents the total amount of money Anthony earns if he runs 10 miles. How much does Anthony earn if he runs 10 miles?
The earnings form an arithmetic sequence: $5, $7, $9, and so on, increasing by $2 per mile. The 10th-mile amount is $5 + 9($2) = $23. The total is 10 times the average of the first and last amounts: 10 × ($5 + $23) ÷ 2 = $140, so Anthony earns 140 dollars.
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