The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. What is the 23rd term?

9 =F + 4D,   
- 84 =F + 31D, solve for F, D

 

F =205/9 - This is the first term
D =- 31/9 - This is the common difference.

 

23rd term =205/9 + (- 31/9 * 22)
                 = - 53