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

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Question 980362: The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. What is the 23rd term?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad
.
.
a%5B5%5D=a%5B1%5D%2B%285-1%29%2Ad
1.a%5B1%5D%2B4d=9
.
.
a%5B32%5D=a%5B1%5D%2B%2832-1%29%2Ad
2.a%5B1%5D%2B31d=-84
.
.
Subtract eq. 1 from eq. 2,
a%5B1%5D%2B31d-a%5B1%5D-4d=-84-9
27d=-93
d=-93%2F27
d=-31%2F9
.
.
So then,
a%5B1%5D%2B4%28-31%2F9%29=9
a%5B1%5D-124%2F9=81%2F9
a%5B1%5D=205%2F9
and
a%5B23%5D=205%2F9%2B%2823-1%29%28-31%2F9%29
a%5B23%5D=205%2F9-682%2F9
a%5B23%5D=-477%2F9
highlight_green%28a%5B23%5D=-53%29