The general term of a sequence is given. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio.
-A pendulum bob swings through an arc 70 inches long on its first swing. Each swing thereafter, it swings only 80% as far as on the previous swing. What is the length of the arc after 8 swings? Round to two decimal places.
A) 14.68 inches
B) 11.74 inches
C) 9.40 inches
D) 392.00 inches

Question

Quizplus · Accepted Answer

The sequence is geometric with a common ratio of 0.8. The length of the arc after 8 swings is found using the formula for the nth term of a geometric sequence: $a_n = a_1 \cdot r^{(n-1)}$, where $a_1 = 70$ inches and $r = 0.8$. For the 8th swing, $a_8 = 70 \cdot 0.8^{(8-1)} = 14.68$ inches.

The General Term of a Sequence Is Given