Final answer:
The value of the common difference in the arithmetic series is approximately 2.862.
Step-by-step explanation:
An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is constant. Let's denote the common difference as 'd'.
Given that u₁ = 4, we know that the first term of the series is 4.
Using the formula for the sum of an arithmetic series, Sₙ = (n/2)(u₁ + uₙ), where Sₙ is the sum of the first 'n' terms of the series, and uₙ is the nth term of the series, we can find the value of 'd' by substituting the given values for S₃₀ and u₁:
1425 = (30/2)(4 + (4 + 29d))
1425 = 15(8 + 4 + 29d)
1425 = 15(12 + 29d)
95 = 12 + 29d
83 = 29d
d ≈ 2.862
Therefore, the approximate value of the common difference is 2.862.