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Mathematics
OpenStudy (anonymous):

HELP HELP HELP . Identify the 27th term of an arithmetic sequence where a1 = 38 and a17 = -74. (2 points) Answer -20.5 -151 -22.75 -144 Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95. (2 points) Answer 203 197 168 163

OpenStudy (netlopes1):

Do you know this equation \[a_{n}=a_{1}+(n-1).r\] all right? So, first question: \[a_{17}=a_{1}+(17-1).r \rightarrow -74 = 38 + 16.r \rightarrow 16.r=-112 \] and r = -7

OpenStudy (netlopes1):

So, \[a_{27}=38+(27-1).(-7) \rightarrow a_{27} = 38 - 182 \rightarrow a_{27} = -144\]

OpenStudy (netlopes1):

Use the same equation to resolve second question: \[a_{18}=a_{1}+(18-1).r \rightarrow 95 = -7 + 17r \rightarrow 102 = 17r \rightarrow r=6\] and..... \[a_{35}=-7+(35-1).6 \rightarrow a_{35} = -7 + 204 \rightarrow a_{35} = 197\]

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