Question

A bungee jumper falls 97.2 feet before bouncing back up at the end of his bungee cord. Then he falls 64.8 feet before bouncing up again. On his third descent, he falls 43.2 feet before going back up. What is the total distance the bungee jumper drops after five falls if the distances continue in this pattern? (Do not include the distance traveled up.)

Answer 1

The difference between jump 1 and jump 2 is 32.4 and the difference between jump 2 and jump 3 is 21.6, which is 2/3 of the first difference. So the difference between jump 3 and jump 4 should be 14.4 and the difference between jump 4 and 5 should be 9.6.  That makes jump 4 28.8 ft and jump 5 19.2 ft.  So we want only the total amount the jumper "falls" so that is 97.2+64.8+43.2+28.8+19.2=253.2.

Answer 2

The total distance the bungee jumper drops after five falls if the distances continue in this pattern is 1282 feet.

A sequence is an arrangement of terms that increase or decrease in order. There are two kinds of sequence;

• Arithmetic progression
• Geometric progression

Looking at the sequence; 97.2, 64.8, 43.2 ...... We can see that the common ratio is 1.5 hence it is a geometric sequence.

The sum of the first five terms of the sequence is;

S5 = a(r^n -1)/r - 1

S5 = 97.2(1.5^5 - 1)/1.5 -1

S5 = 1282 feet

Learn more about geometric sequence: https://brainly.com/question/11266123