Solve the problem.
-While bungee jumping, Gregory falls from a height of 80 feet. He continues to bounce one-half the height from which he last fell. Write out the first five terms of this geometric sequence and find the general term.
A) $40,20,10,5 , \frac { 5 } { 2 } ; a _ { n } = \frac { 80 } { 2 ^ { n - 1 } }$
B) $80,40,20,10,5 ; a _ { n } = \frac { 80 } { 2 ^ { n - 1 } }$
C) $80,78,76,74,72 ; a _ { n } = 80 - 2 ( n - 1 )$
D) $80,40,20,10,5 ; a _ { n } = \frac { 80 } { 2 ^ { n } }$

Question

Quizplus · Accepted Answer

The first term is 80 feet (the initial height from which Gregory falls). Each subsequent term is half the previous term, resulting in a geometric sequence: 80, 40, 20, 10, 5. The general term for a geometric sequence is given by $a_n = a_1 \cdot r^{(n-1)}$, where $a_1$ is the first term and $r$ is the common ratio. Here, $a_1 = 80$ and $r = \frac{1}{2}$, so the general term is $a_n = 80 \cdot (\frac{1}{2})^{(n-1)} = \frac{80}{2^{n-1}}$.

Solve the Problem 40,20,10,5,52;an=802n−140,20,10,5 , \frac { 5 } { 2 } ; a _ { n } = \frac { 80 } { 2 ^ { n - 1 } }40,20,10,5,25​;an​=2n−180​

Solve the Problem $40,20,10,5 , \frac { 5 } { 2 } ; a _ { n } = \frac { 80 } { 2 ^ { n - 1 } }$