Final answer:
The explicit rule for the arithmetic sequence with a4=24 and a17=-4 is found by first calculating the common difference and then the first term. The common difference is -28/13, and the first term is 396/13. The explicit rule is an = 396/13 - (n - 1)(28/13).
Step-by-step explanation:
To write an explicit rule for the arithmetic sequence given that a4 = 24 and a17 = -4, we first need to find the common difference, d, and then use it to write the rule.
Firstly, we calculate the common difference using the given terms:
- The difference in term position is 17 - 4 = 13 steps.
- The difference in term value is -4 - 24 = -28.
- Thus, the common difference d = (-28) / 13 = -28/13.
Now that we have d, we can find the first term, a1, using one of the given terms. Let's use a4 = 24:
- a4 = a1 + (4 - 1) × d
- 24 = a1 + 3 × (-28/13)
- 24 = a1 - 84/13
- a1 = 24 + 84/13
- a1 = (312/13) + (84/13)
- a1 = 396/13
Finally, the explicit rule for the arithmetic sequence is an = a1 + (n - 1)d. Plugging in the values we found:
an = 396/13 + (n - 1)(-28/13)
an = 396/13 - (n - 1)(28/13)