At the local bunny-hop, Mr. Meyering jumps 20 inches on his first jump and then 10 inches with his second jump. If the distances form a geometric sequence,

Question

At the local bunny-hop, Mr. Meyering jumps 20 inches on his first jump and then 10 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 general formula for finding the sum of an infinite geometric series is S = a1/(1-r), where S is the sum of the infinete series, a1 is the first term of the series, and r is the common ratio.

In the given case if bunny-hop a1=20 inches and r = a2/a1 where a2 is thr second term or the didtance covered in second jump while a1 is the distance covered in the first jump. So a2=10 and a1 = 20, therefore r = 10/20 = 1/2.

Plugging the values of a1 and r in the forumla of sum of infinite geometric sequence S = 20 /(1-1/2) = 20/(1/2)

= 40 inches

The total distance Mr. Meyering jumps is 40 inches.

Answer 2

sum = a1/(1-r) = 20/(1-1/2) = 20/(1/2) = 20(2) = 40

20+10+5+5/2 + 5/4 + 5/8 + ... = 40