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In an arithmetic sequence,
a_(17) = -40 and
a_(28) = -73. Explain how to use this information to write a recursive formula for this sequence.

User Tymel
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1 Answer

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The common difference is equal the difference between the given terms divide by the difference between the term numbers:


d=(a_(28)-a_(17))/(28-17)\to d=(-73-(-40))/(11)=(-33)/(11)=-3

Calculate the first term:


a_1=a_(17)-16d\\\\a_1=-40-16(-3)=-40+48=8

The recursive formula is:


a_n=\left\{\begin{array}{ccc}a_1=8\\a_(n+1)=a_n-3\end{array}\right

User Viacheslav
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