+41 The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. What is the 23rd term?
+781 Use the equation for a term of an arithemetic sequence: a+d(n-1), where a is the first term, r is the common difference, and n is the term you are trying to find the value of.
From the first sentence we form the equation:
a+d(4)=9--->a+4d=9
a+d(31)=-84--->a+31d=-84
Now we have a system of equations and solve to get a=205/9 and d=-31/9.
So the 23rd term is
205/9-31/9(23-1)
=205/9-31/9*22
=-53
