Final answer:
The function to determine the nth term of the arithmetic sequence is f(n) = 3n - 12. This was derived by determining the common difference to be 3 and calculating the first term as being -9. Therefore correct option is A
Step-by-step explanation:
The given problem involves finding a function that can determine the nth term of an arithmetic sequence, where we are given the 20th term (48) and the 25th term (63). To find the common difference, we subtract the 20th term from the 25th term and divide by the number of terms between them:
d = (63 - 48) / (25 - 20) = 15 / 5 = 3
With the common difference (d) of 3, we can now express the nth term of the sequence as:
f(n) = a + (n - 1)d
To find 'a', the first term, we use the 20th term provided:
48 = a + (20 - 1) × 3
a = 48 - 57 = -9
So, the nth term formula for the sequence is:
f(n) = -9 + (n - 1) × 3
f(n) = 3n - 12
Hence, the correct function among the options provided is:
A. f(n) = 3n - 12