Question

A recursive rule for an arithmetic sequence is a₁=4;a_n=a_(n−1)−3 .

What is the explicit rule for this sequence?




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a_n=

Answer 1

The explicit formula of the arithmetic sequence:

`a_n=a_1+(n-1)d`

d - common difference

We have the recursive formula of an arithmetic sequence:

`\left\{\begin{array}{ccc}a_1=4\\a_n=a_(n-1)-3\end{array}\right`

Therefore we have:

`a_1=4,\ d=-3`

Substitute:

`a_n=4+(n-1)(-3)=4-3n+3=7-3n`

Answer: aₙ = 7 - 3n