Answer:
The Recursive Formula for the sequence is:
; a₁ = 125
Hence, option D is correct.
Step-by-step explanation:
We know that a geometric sequence has a constant ratio 'r'.
The formula for the nth term of the geometric sequence is

where
aₙ is the nth term of the sequence
a₁ is the first term of the sequence
r is the common ratio
We are given the explicit formula for the geometric sequence such as:

comparing with the nth term of the sequence, we get
a₁ = 125
r = 1/5
Recursive Formula:
We already know that
We know that each successive term in the geometric sequence is 'r' times the previous term where 'r' is the common ratio.
i.e.

Thus, substituting r = 1/5
and a₁ = 125.
Therefore, the Recursive Formula for the sequence is:
; a₁ = 125
Hence, option D is correct.
Here, we can set up a proportion:
34 ÷ 3/4 = ? ÷ 1
34*1 = 34
34÷3/4 = the time needed to build one toyboat
34/3/4 = 45.3333333333
45.3 repeating is not a whole number, so we need to approximate.
45 is the closest whole number,
So.. a machine can paint 45 toy boats per hour.
I really hope that helped! :)