2021 AMC 10A Problems/Problem 4
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Problem 4
A cart rolls down a hill, travelling inches the first second and accelerating so that during each successive
-second time interval, it travels
inches more than during the previous
-second interval. The cart takes
seconds to reach the bottom of the hill. How far, in inches, does it travel?
Solution
Since we seek the sum
in which there are 30 addends. The last addend is
Therefore, the requested sum is
Recall that to find the sum of an arithmetic series, we take the average of the first and last terms, then multiply by the number of terms, namely
Video Solution (Using Arithmetic Sequence)
~ pi_is_3.14