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# Artitmetic sequence question

+1
293
2
+117

In this particular arithmetic sequence, a8 = 28 and a16 = 108. What is the value of a24?

a24 = 188

a24 = 162

a24 = 198

a24 = 224

I know it's not B

failurewithasmile  Apr 14, 2017
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#1
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188    ...........

Guest Apr 14, 2017
#2
+17711
+3

The general formula is:  an  =  a1 + (n - 1)d

a8 = 28         --->     a8  =  a1 + (8 - 1)d        --->        28  =  a+ 7d

a16 = 108     --->     a16  =  a1 + (16 - 1)d     --->     108  =  a1 + 15d

Subtract down the columns:                                    -80  =        - 8d

--->          d  =  10

Substituting this value for d into the first equation:  28  =  a+ 7d

--->       28  =  a+ 7(10)

--->       28  =  a+ 70

--->        a1  =  -42

So the equation is:  an  =  -42 + (n - 1)(10)

To find a24, substitue 24 in for n and solve.

geno3141  Apr 14, 2017

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