Question

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

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