Answer: To find the explicit rule for the sequence 13, 10.5, 8, 5.5, 3, 0.5, we can look for a common difference between successive terms. Subtracting any term from the previous term, we get:
10.5 - 13 = -2.5
8 - 10.5 = -2.5
5.5 - 8 = -2.5
3 - 5.5 = -2.5
0.5 - 3 = -2.5
Since the common difference is -2.5, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
where a1 is the first term and d is the common difference. Substituting the values we have:
a1 = 13
d = -2.5
So the explicit rule for the sequence is:
an = 13 - 2.5(n-1)
Simplifying:
an = 15 - 2.5n
Explanation: