SOLUTION: 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 hi

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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.
a) 265 b) 283 c) 319 d) 337 e) 378
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
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. 

This is the sum of an arithmetic series with common
difference d=5, first term a%5B1%5D=4 and 
number of terms n=11.  The formula for the sum 
is:

S%5Bn%5D=%28n%282a%5B1%5D%2B%28n-1%29%2Ad%29%29%2F2

S%5B11%5D=%2811%282%2A4%2B%2811-1%29%2A5%29%29%2F2 

S%5B11%5D=%2811%288%2B10%2A5%29%29%2F2

S%5B11%5D=%2811%288%2B50%29%29%2F2

S%5B11%5D=%2811%2858%29%29%2F2

S%5B11%5D=%2811%28cross%2858%29%5E29%29%29%2Fcross%282%29

S%5B11%5D=11%2A29

S%5B11%5D=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