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# quiz quetions

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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
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#1
+25995
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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
+75344
+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

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

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