Final answer:
The nth term of the given geometric sequence is an = 0.6 × 5n-1. The sixth term (a6) is 937.5 when rounding is not required.
Step-by-step explanation:
To write an equation for the nth term of the geometric sequence 0.6, 3, 15, -- 75, ..., we first need to determine the common ratio (r). By dividing any term by the preceding term, we can find that r = 3 / 0.6 = 5. Now, the nth term of a geometric sequence is given by an = a1 × rn-1, where a1 is the first term and r is the common ratio.
So the equation for the nth term is an = 0.6 × 5n-1. To find the sixth term (a6), we just substitute n = 6 into the equation:
a6 = 0.6 × 56-1 = 0.6 × 55
The solution is a6 = 937.5, which is 75 multiplied by the common ratio 5 once more (since 75 is the fifth term).