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53
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avatar+42 

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

 Apr 26, 2020
 #1
avatar+485 
+1

Let a be the first term, and r be the rate of the arithmetic sequence. We have:

 

a + 4r = 9

a + 31r = -84

a + 22 r = ?

Realize that we can Subtract our first equation from our second equation. This gives us:

 

27r = -93

r = -93/27

 

since we already have that a+31r = -84, we can just subtract 9r from this equation to get:
 

a + 22r = -84 -(9*-93/27) = -84 -(-31) = -84 + 31 = -53

 Apr 26, 2020
 #2
avatar
0

Do u take algebra 2 classes at Santa Clara AOPS, because this looks like one of the homework questions.

 Apr 27, 2020
 #3
avatar+109527 
0

It looks like a standard question that you could find in any school.

There is nothing unusual about this question.

 Apr 27, 2020

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