Precalculus, Chapter 9, 9.2, Section 9.2, Problem 26

The given first few terms of the arithmetic sequence are:
{10, 5, 0, -5, -10...}
Take note that the nth term of an arithmetic series is a_n =a_1 + (n-1)d . Since the first term a_1 is known already, let's solve for the value of d. d is the common difference of the consecutive terms of an arithmetic sequence.
d=a_2-a_1 = 5-10=-5
d=a_3-a_2 = 0 - 5 = -5
d=a_4-a_3=-5-0 = -5
d=a_5-a_4 = -10 - (-5)=-5
So the common difference is d = -5.
Then, plug-in a_1=10 and d=-5 to the formula of nth term of arithmetic sequence.
a_n =a_1 + (n-1)d
a_n=10 + (n-1)(-5)
a_n = 10 -5n + 5
a_n=15-5n
Therefore, the nth term of the given arithmetic sequence is a_n=15 - 5n .