Final answer:
To show that a2/1, a2/2, a2/3, ... is a geometric sequence, we substitute the values of a and r into the formula for the original sequence. The terms a2/1, a2/2, a2/3, ... form a geometric sequence with a common ratio of 1/2.
Step-by-step explanation:
To show that a2/1, a2/2, a2/3, ... is a geometric sequence, we need to find its common ratio.
Since the original sequence is a geometric sequence with initial term a and common ratio r, we have:
a1 = a
a2 = ar
a3 = ar2
...
To find the terms a2/1, a2/2, a2/3, ..., we can substitute a = a2 and r = 1/2 into the formula for the original sequence:
an = ar(n-1)
Substituting a = a2 and r = 1/2:
a2/1 = a2 x (1/2)0 = a2
a2/2 = a2 x (1/2)1 = a2/2
a2/3 = a2 x (1/2)2 = a2/4
...
Thus, the terms a2/1, a2/2, a2/3, ... form a geometric sequence with a common ratio of 1/2.