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30 votes
What is an explicit formula for an arithmetic sequence with a common difference of three and whos second term is nine?

User SuddenMoustache
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2 Answers

14 votes
14 votes
  • First term =9-3=6
  • Second term=9
  • Common difference=3

So

  • a=6
  • d=3

Explicit formula


\\ \rm\Rrightarrow a_n=a+(n-1)d


\\ \rm\Rrightarrow a_n=6+3(n-1)

User Ed R
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3.4k points
16 votes
16 votes

Answer:


\sf a_n=3n+3

Explanation:

An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.

A recursive formula for an arithmetic sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.

Explicit formula


\sf a_n=a+(n-1)d

where:


  • \sf a_n is the nth term
  • a is the first term
  • n is the number of the term
  • d is the common difference

Given:


  • \sf a_2=9
  • d = 3
  • n = 2

Substituting these values into the formula to find a:


\implies \sf 9=a+(2-1)3


\implies \sf 9=a+3


\implies \sf a=6

Therefore the formula is:


\implies \sf a_n=6+(n-1)3


\implies \sf a_n=6+3n-3


\implies \sf a_n=3n+3

User Guy Thomas
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2.9k points