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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?

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DᴀʀᴋPᴀʀᴀᴅᴏxid

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

[tex] \textbf{Let's see if the sequence is Arithmetic :} [/tex]

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

  • [tex] \textsf{-34 - (-29) = -5 } [/tex]

  • [tex] \textsf{-39 - (-34) = -5 } [/tex]

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

Fieryanswererftid

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, [tex]\boxed{\sf \bold{second \ term = \dfrac{first \ term+third \ term}{2} }}[/tex]

If the sequence is geometric, [tex]\boxed{\sf \bold{second \ term = \sqrt{first \ term \ x \ third \ term} }}[/tex]

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

Check for arithmetic

[tex]\rightarrow \sf -34 = \sf \dfrac{-29 +(-39)}{2}[/tex]

[tex]\rightarrow \sf -34 = \sf \dfrac{-68}{2}[/tex]

[tex]\rightarrow \sf -34 = -34[/tex]       [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

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