Answer:
The correct statement is:
The sequence is not geometric because 2/3 was added to each term to get the next term.
Step-by-step explanation:
Vince wrote the sequence below.
1/3, 1, 5/3, 7/3...
the sequence could also be written as:
1/3,3/3,5/3,7/3,.....
Let [tex]a_n[/tex] represents the nth term of the sequence.
now the first term of the sequence is:
[tex]a_1=\dfrac{1}{3}[/tex]
second term is:
[tex]a_2=\dfrac{3}{3}[/tex]
which could also be obtained as:
[tex]a_2=a_1+\dfrac{2}{3}[/tex]
Third term is:
[tex]a_3=\dfrac{5}{3}[/tex]
which could also be obtained as:
[tex]a_3=a_2+\dfrac{2}{3}[/tex]
Fourth term is:
[tex]a_4=\dfrac{7}{3}[/tex]
which could also be obtained as:
[tex]a_4=a_3+\dfrac{2}{3}[/tex]
The correct reason that explains that the given sequence is geometric or not is:
The sequence is not geometric because 2/3 was added to each term to get the next term.
(Hence such a sequence is not geometric but an arithmetic sequence with common difference of 2/3)
