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)

23rd term = -53