Question

An arithmetic sequence has this recursive formula:

What is the explicit formula for this sequence?

Answer 1

Answer:

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

Step-by-step 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 ...

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