An arithmetic sequence can be expressed as:
a(n)=a+d(n-1), where a(n) is the value of the nth term, a is the initial term, d is the common difference, and n is the term number....we are given to terms...
8=a+d(5-1) and -7=a+d(10-1) so
8=a+4d and -7=a+9d
So if we get the difference of these two equations we have:
15=-5d, so d=-3
We again use one of the original equations to solve for the first term and using the common difference d that we just found...
8=a-3(5-1)
8=a-12, so a=20, so are sequence has the rule:
a(n)=20-3(n-1) or more neatly:
a(n)=23-3n so
a(100)=-277
a(500)=-1477