The sum of the first five terms of an arithmetic series is zero . The 5th term is 6.determine the first term and the common difference

Question

It's out of 8 marks

Answer 1

First 5 terms:

a,

a+d,

a+2d,

a+3d,

a+4d

———

5a+10d is the sum=0

a+4d=6, so a=6-4d. Substitute this in the other equation: 5(6-4d)+10d=0,

30-20d+10d=30-10d=0, so 10d=30, d=30/10=3; a=6-4×3=6-12=-6.

CHECK

-6, -3, 0, 3, 6 sum to zero when the first term is -6 and the common difference is 3.