The recursive formula of the explicit rule an = (n + 1)² is where a1 = 4
The explicit formula is given as:
an = (n + 1)²
This means that:
a1 = (1 + 1)² = 4
a₂ = (2 + 1)² = 9
a₃ = (3 + 1)² = 16
Rewrite as:
a₂ = 4 + 2 * 2 + 1 = 9
a₃ = 9 + 2 * 3 + 1 = 16
Substitute a₂ = 9
a₃ = a₂ + 2 * 3 + 1 = 16
Express 2 as 3 - 1
a₃ = a₃₋₁ + 2 * 3 + 1
Express 3 as n
Evaluate the product
Hence, the recursive formula of the explicit rule an = (n + 1)² is where a1 = 4
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Using integration, it is found that the area between the two curves is of 22 square units.
<h3>What is the area between two curves?</h3>The area between two curves y = f(x) and y = g(x), in the interval from x = a to x = b, is given by:
In this problem, we have that:
.
Hence, the area is:
Applying the Fundamental Theorem of Calculus:
The area between the two curves is of 22 square units.
More can be learned about the use of integration to find the area between the two curves at brainly.com/question/20733870