paynelove19
Answered

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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.

1, 3, 6, 10, 15, …
My answer below:
3 + 1 = 4
3 - 6 = -3
so, I get neither?

Sagot :

fieryanswererft

Sequence: 1, 3, 6, 10, 15, …

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

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

Check for arithmetic:

[tex]\sf \rightarrow 3 = \dfrac{1+6}{2}[/tex]

[tex]\sf \rightarrow 3 =3.5[/tex]    Hence, the sequence is not arithmetic

Check for geometric:

[tex]\sf \rightarrow 3 = \sqrt{1*6}[/tex]

[tex]\sf \rightarrow 3 = \sqrt{6}[/tex]   Hence, the sequence is not geometric

Solution:

  • Neither
DᴀʀᴋPᴀʀᴀᴅᴏx

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

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

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

[tex] \textsf{and} [/tex]

  • [tex] \textsf{If the ratio of successive terms is } [/tex] [tex] \textsf{equal then, the terms are in GP} [/tex]

[tex]\textsf{Since neither common difference is same, }[/tex] [tex]\textsf{nor common ratio is same, therefore }[/tex] [tex] \textsf{we can infer that it's neither an Arithmetic progression} [/tex] [tex] \textsf{nor Geometric progression. } [/tex]

Hope it helps ~

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