All of the given questions(#71 to #75) are GP(s).
Formula to be used: a(n) = a(1) * r^(n - 1)
Pronounced as:
nth term = 1st term * r^(n - 1), where r is the common difference.
*r = ratio of any two consecutive terms.
71):
1st term = 2, r = 4/2 = 2
Therefore,
11th term = 2 * 2^(11 - 1) = 2 * 1024 = 2048
72):
1st term = 1, r = 4/1 = 4
Therefore,
9th term = 1 * 4^(9 - 1) = 1 * 4^8 = 65536
73):
1st term = 1, r = (1/2)/1 = 1/2
Therefore,
12th term = 1 * (1/2)^(12 - 1)= (1/2)^11 = 2^(-11)
12th term = 1/2^11 = 1/2048
74):
1st term = 1, r = (1/3)/1= 1/3
Therefore,
10th term = 1 * (1/3)^(10 - 1) = 1/3^9 = 3^(-9)
10th term = 1/3^9 = 1/19683
75):
1st term = 40, r = 10/40 = 1/4
Therefore,
8th term = 40 * (1/4)^(8 - 1) = 40/4^7 = 10/4^6 = 5/2048
76):
1st term = 10, r = 2/10 = 1/5
Therefore,
9th term = 10 * (1/5)^(9 - 1) = 10/5^8 = 2/5^7
9th term = 2/78125
