Question

A recursive rule for an arithmetic sequence is a1=4;an=an−1+3 . What is an explicit rule for this sequence? Enter your answer in the box. an=

Answer 1

Answer:

$a_{n}=4+3(n-1)$

Step-by-step explanation:

The given recursive rule is

$a_{1}=4\\a_{n}=a_{n-1}+3$

According to this recursive rule, the sequence is

$4, 7, 10, 13, 16, 19,...$

Because, the recursive rule states that each new term must be 3 units greater.

Now, an explicit form of this sequence could be found using this formula

$a_{n}=a_{1}+(n-1)d$

Where $d=3$ and $a_{1}=4$

Replacing these values, we have

$a_{n}=4+3(n-1)$

Therefore, the explict form is $a_{n}=4+3(n-1)$, which can be used to find any tem of the arithmetic sequence.

Answer 2

Answer:

an=3n+1

Step-by-step explanation: