The fifth and tenth term of an A. P are 8 and - 7 respectively. Find the 100th and 500th term of the A. P

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