Arithmetic

Question

The sum of the first five terms of an arithmetic sequence is 0 and the fifth term is 8 .determine the common difference and the first term

Answer 1

The first 5 terms can be written:

a,a+d,a+2d,a+3d, a+4d where a is the first term and d is the difference.

So a+4d=8 (5th term) and

5a+10d=0 (sum of first 5 terms).

Therefore 5a=-10d, a=-2d.

So -2d+4d=8, 2d=8, d=4, making a=-8.

The series is:

-8, -4, 0, 4, 8,... First term: -8, difference=4.