Question 234484
A boy on a bicycle coasts down a hill. covering 4 feet the first second and in each succeeding second 5 feet more than in the preceding second . if he reaches the bottom of the hill in 11 seconds, find the total distance (in feet) traveled. 
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This is the sum of an arithmetic series with common
difference {{{d=5}}}, first term {{{a[1]=4}}} and 
number of terms {{{n=11}}}.  The formula for the sum 
is:

{{{S[n]=(n(2a[1]+(n-1)*d))/2}}}

{{{S[11]=(11(2*4+(11-1)*5))/2}}} 

{{{S[11]=(11(8+10*5))/2}}}

{{{S[11]=(11(8+50))/2}}}

{{{S[11]=(11(58))/2}}}

{{{S[11]=(11(cross(58)^29))/cross(2)}}}

{{{S[11]=11*29}}}

{{{S[11]=319}}}, choice (c).

Or, doing it like a kid in elementary school would do it,
which, of course, your teacher would not accept:

4+9+14+19+24+29+34+39+44+49+54 = 319

Edwin</pre>