Question 1162999
What is the common difference? An arithmetic series has 9 terms with a sum of -135. It has the first term of 9. 
<pre>Sum-of-an-A.P. formula: {{{matrix(1,3, S[n], "=", (n/2)(2a[1] + (n - 1)d))}}}
{{{matrix(1,3, S[9], "=", (9/2)(2(9) + (9 - 1)d))}}} -- Substituting {{{matrix(2,3, 9, for, n, 9, for, a[1])}}} 
{{{matrix(1,3,  - 135, "=", (9/2)(18 + 8d))}}} ------- Substituting {{{matrix(1,3, - 135, for, S[9])}}}
- 270 = 9(18 + 8d) ------- Cross-multiplying
{{{matrix(1,3, (- 270)/9, "=", 18 + 8d)}}}
- 30 = 18 + 8d ====> - 48 = 8d 
Common difference, or {{{highlight_green(matrix(1,5, d, "=", (- 48)/8, "=", - 6))}}}