Final answer:
The 24th term of the arithmetic progression is 73.
Step-by-step explanation:
To find the 24th term of an arithmetic progression, we need the common difference (d) and the first term (a). We can find the common difference using the formula:
d = (10th term - 4th term) / (10 - 4) = (31 - 13) / 6 = 18 / 6 = 3
Now that we have the common difference, we can find the first term by substituting the values of the 4th term, 10th term, and the common difference into the formula:
13 = a + 3(4 - 1)
13 = a + 9
a = 13 - 9 = 4
Using the formula for the nth term of an arithmetic progression:
24th term = a + (24 - 1)d = 4 + (24 - 1)(3) = 4 + 23(3) = 4 + 69 = 73