Final answer:
To calculate S₂₃, we first determined the first term of the arithmetic sequence, found it to be 12, then used the summation formula to find that S₂₃ = 883.2.
Step-by-step explanation:
The student is asked to calculate S₂₃, which is the sum of the first 23 terms of an arithmetic sequence. The given information is a₆ = 24 (the sixth term of the sequence) and the common difference is d = 2.4. To find S₂₃, we first need to find the first term of the sequence (a₁). We can use the formula for the n-th term of an arithmetic sequence: aₙ = a₁ + (n - 1)d. Plugging in the values we have, we get 24 = a₁ + (6 - 1)× 2.4. Solving for a₁, we find that a₁ = 24 - 5× 2.4 = 24 - 12 = 12.
Now, to calculate the sum S₂₃, we use the summation formula for the first n terms of an arithmetic sequence: Sₙ = ⅓n (2a₁ + (n - 1)d). Therefore, S₂₃ = ⅓(23) (2× 12 + (23 - 1)× 2.4) = ⅓(23) (24 + 22× 2.4) = ⅓(23) (24 + 52.8) = ⅓(23) × 76.8 = 23 × 38.4 = 883.2.
Thus, the correct answer is c. 883.2.