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 numberwe 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