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Determine whether each of the following sequences are arithmetic, geometric or neither. If arithmetic, state the common difference. If geometric, state the common ratio.

4, 13/3, 14/3, 5, 16/3, …

Is the answer: Neither?

User Buran
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2 Answers

5 votes
5 votes

Answer:

Arithmetic with common difference of
\sf (1)/(3)

Explanation:


\textsf{Given sequence}=4, (13)/(3), (14)/(3), 5, (16)/(3),...

If a sequence is arithmetic, the difference between consecutive terms is the same (this is called the common difference).

If a sequence is geometric, the ratio between consecutive terms is the same (this is called the common ratio).


\sf 4\quad \overset{+(1)/(3)}{\longrightarrow}\quad(13)/(3)\quad \overset{+(1)/(3)}{\longrightarrow}\quad (14)/(3)\quad \overset{+(1)/(3)}{\longrightarrow}\quad 5\quad \overset{+(1)/(3)}{\longrightarrow}\quad (16)/(3)

As the difference between consecutive terms is
\sf (1)/(3) then the sequence is arithmetic with common difference of
\sf (1)/(3)

General form of an arithmetic sequence:
\sf a_n=a+(n-1)d

where:


  • \sf a_n is the nth term
  • a is the first term
  • d is the common difference between terms

Given:

  • a = 4

  • \sf d=(1)/(3)

So the formula for the nth term of this sequence is:


\implies \sf a_n=4+(n-1)(1)/(3)


\implies \sf a_n=(1)/(3)n+(11)/(3)

User Dimirc
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\qquad\qquad\huge\underline{{\sf Answer}}


\textbf{Let's see if the sequence is Arithmetic or Geometric :}


\textsf{If the difference between successive terms is }
\textsf{equal then, the terms are in AP}


  • \sf{ (14)/(3)- (13)/(3) = (1)/(3)}


  • \sf{ {5}{}- (14)/(3) = (15-14)/(3) =(1)/(3)}


\textsf{Since the common difference is same, }
\textsf{we can infer that it's an Arithmetic progression}
\textsf{with common difference of } \sf (1)/(3)

User TheMrbikus
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