SOLUTION: Determine if the sequece is arithmetic. If the sequence is arithmetic, find the common difference. a_n = n(n+9)

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Question 1096859: Determine if the sequece is arithmetic. If the sequence is arithmetic, find the common difference.
a_n = n(n+9)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Plug in n = 1 to find the first term

a%5Bn%5D+=+n%28n%2B9%29

a%5B1%5D+=+1%281%2B9%29 n is replaced with 1

a%5B1%5D+=+1%2810%29

a%5B1%5D+=+10

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Plug in n = 2 to find the second term

a%5Bn%5D+=+n%28n%2B9%29

a%5B2%5D+=+2%282%2B9%29 Substitute 2 for n

a%5B2%5D+=+2%2811%29

a%5B2%5D+=+22

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Plug in n = 3 to find the third term

a%5Bn%5D+=+n%28n%2B9%29

a%5B3%5D+=+3%283%2B9%29

a%5B3%5D+=+3%2812%29

a%5B3%5D+=+36

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Subtract the second and first terms:

d%5B1%5D+=+a%5B2%5D+-+a%5B1%5D+=+22+-+10+=+12

Now subtract the second and third terms

d%5B2%5D+=+a%5B3%5D+-+a%5B2%5D+=+36-22+=+14

Since d%5B1%5D+%3C%3E+d%5B2%5D this means we do not have an arithmetic sequence.