Question

An arithmetic sequence has this recursive formula:

What is the explicit formula for this sequence?

Answer 1

`\text{\bf{C.}}\quad a_n=4+(n-1)(-7)`

Explanation:

An arithmetic sequence that is described by the explicit formula ...

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

can also be described by the recursive formula ...

`\left \{\begin{array}{l}a_1=\text{(first term)}&a_n=a_(n-1)+d&\end{array}\right.`

Matching parts of the formulas, we see that a1 = 4, d = -7. Putting these values into the explicit formula gives ...

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