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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=

User Milesmeow
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2 Answers

6 votes

Answer:

an=3n+1

Explanation:

User Gabriel Staples
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Answer:


a_(n)=4+3(n-1)

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.

User Imricardoramos
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