JAMB 1988 · UME · Q28

If the sum of the 8th and 9th terms of an arithmetic progression is 72 and the 4th term is $-6$ , find the common difference.

Worked solution (try it first)

The 8th and 9th terms are $a + 7d$ and $a + 8d$ , so their sum gives $2a + 15d = 72$ .
The 4th term gives $a + 3d = -6$ .
Double it: $2a + 6d = -12$ .
Subtract the second equation from the first: $9d = 72 - (-12) = 84$ .
So $d = \frac{84}{9} = 9\frac13$ , option D.