A geometric sequence is defined by the recursive formula
t1 = 64, tn= tn-1/2 where n ∈N and n > 1. The sequence is
A)-64, -16, -8, -4, -2, -1, ...
B)64, 16, 8, 4, 2, 1, ...
C)64, 32, 16, 8, 4, 2, ...
D)64, 128, 256, 512, 1024, 2048, ...
The answer is C :)
correct, though your notation makes it unclear. Better would be
t_n = t_n-1 / 2
or
t_(n) = t_(n-1) / 2
t(n) = t(n-1)/2
or t(n) = (t(n-1))/2
sometimes parens or spacing make your intentions clearer
To determine the correct answer, we need to apply the recursive formula to find the terms of the sequence.
Given that t1 = 64 and tn = tn-1/2, we can find the values of tn for n > 1 by repeatedly applying the formula.
For n = 2:
t2 = t1/2 = 64/2 = 32
For n = 3:
t3 = t2/2 = 32/2 = 16
For n = 4:
t4 = t3/2 = 16/2 = 8
For n = 5:
t5 = t4/2 = 8/2 = 4
For n = 6:
t6 = t5/2 = 4/2 = 2
Based on this pattern, we can see that the terms are halving at each step, indicating that the common ratio is 1/2.
The correct answer is the option C: 64, 32, 16, 8, 4, 2, ...