Question 1078519
On the first swing, the distance traveled is 100, and on the second swing, the distance is 99.
The first term of the geometric sequence is, a1 = 100
The second term of the sequence is, a2 = 99
The common ratio r = 99/100
Therefore, the expression for the n-th term of the sequence is: 
a_n = 100*(99/100)^(n-1)
(a) To answer a, we need to find the value of n for which a_n < 50:
50 = 100*(99/100)^(n-1) 
log(1/2)/log(99/100) = n - 1
This gives n = 69.97, and rounding up to the next integer gives n = 70.
(b) Theoretically, using this formula, it would take an infinite number of trips to come to rest.
Hence we need to find the sum of the series a_n = 100*(99/100)^(n-1) from n=1 to n=infinity.
The sum of an infinite series is given by S = a/(1-r) where a=the first term and r=the common ratio.
Therefore, the total distance traveled is S = 100/(1-(99/100) = 100/0.01 = 10,000 cm.