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What’s the recursive and explicit formula for an arithmetic sequence we a1=2 and d=-4 ?

User Bmkrio
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The explicid formula of an arithmetic sequence:


a_n=a_1+(n-1)d

We have


a_1=2,\ d=-4

Substitute:


a_n=2+(n-1)(-4) use distributive property


a_n=2+(-4n)+(-1)(-4)\\\\a_n=2-4n+4\\\\\boxed{a_n=6-4n}

The recursive formula of an arithmetic sequence:


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

Substitute:


\left\{\begin{array}{ccc}a_1=2\\a_n=a_(n-1)-4\end{array}\right

User Brynjar
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