Final answer:
To find the explicit formula of an arithmetic sequence, set up two equations using the given terms and the general formula. Solve the system of equations to find the common difference and first term. Substitute the values back into the general formula to get the explicit formula.
Step-by-step explanation:
To determine the explicit formula of an arithmetic sequence, we need to find the common difference (d) and the first term (a1). Using the given information, we can create two equations to solve for these values:
Equation 1: a3 = a1 + 2d = 9
Equation 2: a6 = a1 + 5d = 24
We can solve this system of equations by subtracting Equation 1 from Equation 2 to eliminate a1:
a6 - a3 = (a1 + 5d) - (a1 + 2d)
24 - 9 = 5d - 2d
15 = 3d
d = 5
Substituting the value of d back into Equation 1 or Equation 2, we can solve for a1:
a1 = 9 - 2(5) = -1
The explicit formula for this arithmetic sequence is an = -1 + 5(n - 1)