Answer:
To find the explicit formula for the sequence, we need to determine the common ratio between each term.
The common ratio is found by dividing any term by the previous term. For example:
The common ratio between the second and first terms is 150/30 = 5.
The common ratio between the third and second terms is 750/150 = 5.
Since the common ratio is the same for all terms, we can use it to find any term in the sequence.
Let's call the first term a₁, and let r be the common ratio. Then we have:
a₁ = 30
a₂ = a₁ * r = 30 * 5 = 150
a₃ = a₂ * r = 150 * 5 = 750
a₄ = a₃ * r = 750 * 5 = 3750
a₅ = a₄ * r = 3750 * 5 = 18750
We can see that the explicit formula for the sequence is:
aₙ = a₁ * r^(n-1) = 30 * 5^(n-1)
Therefore, the explicit formula for the sequence is aₙ = 30 * 5^(n-1).