Question

For a fund-raiser, anthony earns $5 for the first mile he runs, an additional $7 for the second mile, an additional $9 for the third mile, and so on. the expression represents the total amount of money anthony earns if he runs 10 miles. how much does anthony earn if he runs 10 miles?

Answer 1

$140
If the dollars per mile increases by 2 every mile you would need to find out how much he makes each mile. It goes in order 5,7,9,11,13,15,17,19,21,23

Answer 2

His total earning for 10 miles is $ 140.

Explanation:

Given,

He earns for first miles = $ 5,

Since, he earns an additional $7 for the second mile, an additional $9 for the third mile, and so on

That is, his earning for second miles = $ 7,

For third miles = $ 9,

For fourth miles = $ 11 ,

..............So, one...

So, we get a sequence,

5, 7, 9, 11, ..........

Which is an A.P.

Having first term, a = 5,

common difference, d = 2,

Number of terms, n = 10

Thus, the sum of the A.P. is,

`S_n=(n)/(2)[2a+(n-1)d]`

[tex]S_{10}=\frac{10}{2}[10+18]=5\times 28 = 140/tex]

Hence, His total earning for 10 miles is $ 140.