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What is the fifth term of the arithmetic sequence whose third term is 29 and whose twenty-ninth term is 289.

Guest Jun 15, 2017
 #1
avatar+26758 
+1

The n'th term of an arithmetic progression is given by a + (n-1)d, where a is the first term and d is the common difference. So here we have:

 

a + (3-1)*d = 29   and

a + (29-1)*d = 289

 

Subtract the first from the second:  26*d = 260   so d = 10

 

Put this in the first equation to get a + 2*10 = 29   so a = 9

 

Hence the fifth term is 9 + (5-1)*10   or 49

.

Alan  Jun 15, 2017
 #2
avatar+87334 
+1

 

Thanks, Alan......here's another approach

 

Common difference  =   [ 29th term - 3rd term] / [ 29 - 3 ]  =

 

 [ 289 - 29 ] / [ 29 - 3 ]  =

 

260 / 26  =   10

 

So....the fifth term is

 

29 + 2(10)  =  49

 

 

 

cool cool cool 

CPhill  Jun 15, 2017
edited by CPhill  Jun 15, 2017
edited by CPhill  Jun 15, 2017

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