At the local bunny-hop, Mr. Meyering jumps 10 inches on his first jump and then 5 inches with his second jump.

Question

At the local bunny-hop, Mr. Meyering jumps 10 inches on his first jump and then 5 inches with his second jump. If the distances form a geometric sequence, what is the total distance Mr. Meyering jumps if he completes infinitely many jumps?

Hint: Use S = a1/ 1-r and remember that |r| must be less than 1.

Answer 1

The sequence is 10(1+1/2+1/4+...) = 10 (sum from 0 to infinity of (1/2)ⁿ

The infinite sum of the series is a/(1-r) where a = 10 and r = 1/2, i.e. 20.

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