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

Guest Oct 1, 2017

Best Answer 

 #2
avatar+88898 
+1

 

We have that

 

a1 + 4d  = 9     and

a1 + 31d = -84       where a1 is the first term  and d is the common difference between terms

 

Subtract both equations

 

- 27d  = 93      divide both sides by -27

 

d = - 93 / 27  = -31/ 9

 

And.....there are 18 terms between the 5th term and the  23rd  term......so we have....

 

9 + 18(-31 / 9)  =  9 - 62   =   -53   =   23rd term

 

 

cool cool cool

CPhill  Oct 1, 2017
 #1
avatar
0

It is -57

Guest Oct 1, 2017
 #2
avatar+88898 
+1
Best Answer

 

We have that

 

a1 + 4d  = 9     and

a1 + 31d = -84       where a1 is the first term  and d is the common difference between terms

 

Subtract both equations

 

- 27d  = 93      divide both sides by -27

 

d = - 93 / 27  = -31/ 9

 

And.....there are 18 terms between the 5th term and the  23rd  term......so we have....

 

9 + 18(-31 / 9)  =  9 - 62   =   -53   =   23rd term

 

 

cool cool cool

CPhill  Oct 1, 2017

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