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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. -29, -34, -39, -44, -49, ...

Is this: common difference =5?
arithmetic?

User Akhilendra
by
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2 Answers

9 votes


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


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


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


  • \textsf{-34 - (-29) = -5 }


  • \textsf{-39 - (-34) = -5 }


\textsf{Since the common difference is same, }
\textsf{we can infer that it's an Arithmetic progression}
\textsf{with common difference of -5}

User Dbaxime
by
7.6k points
1 vote

Sequence: -29, -34, -39, -44, -49, ...

First we need to identify the terms:

  • 1st term = -29
  • 2nd term = -34
  • 3rd term = -39
  • 4th term = -44
  • 5th term = -49

If the sequence is arithmetic,
\boxed{\sf \bold{second \ term = (first \ term+third \ term)/(2) }}

If the sequence is geometric,
\boxed{\sf \bold{second \ term = √(first \ term \ x \ third \ term) }}

=======================================

Check for arithmetic


\rightarrow \sf -34 = \sf (-29 +(-39))/(2)


\rightarrow \sf -34 = \sf (-68)/(2)


\rightarrow \sf -34 = -34 [Hence it's arithmetic series]

To find common difference. we have to think of how to go to next term.

first term: -29

to go the second term, subtract by -5

-29 -5 = -34, second term

-34 - 5 = -39, third term

Hence, common difference: -5

Solutions:

Arithmetic Sequence

Common Difference: -5

User Dawood Awan
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