Apurva0614
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. 4, 13/3, 14/3, 5, 16/3, …​

Sagot :

Answer:

sequence is arithmetic

Step-by-step explanation:

An arithmetic sequence has a common difference between consecutive terms.

A geometric sequence has a common ratio between consecutive terms.

given

4 , [tex]\frac{13}{3}[/tex] , [tex]\frac{14}{3}[/tex] , 5 , that is

[tex]\frac{12}{3}[/tex] , [tex]\frac{13}{3}[/tex] , [tex]\frac{14}{3}[/tex] , [tex]\frac{15}{3}[/tex] , then

[tex]\frac{13}{3}[/tex] - [tex]\frac{12}{3}[/tex] = [tex]\frac{14}{3}[/tex] - [tex]\frac{13}{3}[/tex] = [tex]\frac{15}{3}[/tex] - [tex]\frac{14}{3}[/tex] = [tex]\frac{1}{3}[/tex]

there is a common difference d = [tex]\frac{1}{3}[/tex] between consecutive terms

thus the sequence is arithmetic

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