Question

Vince wrote the sequence below.

Answer 1

Let's rewrite the given sequence :1/3, 1, 5/3, 7/3 . Notice that 1 =3/3, then

1/3, 3/3, 5/3, 7/3,...We also notice that the common difference d is equal to:
3/3 - 1/3 = 2/3 and 5/3 - 3/3 = 2/3 & 7/3 - 5/3 = 2/3

Hence this sequence is NOT A GEOMETRIC PROGRESSION but               an ARITHMETIC PROGRESSION,instead with d = 2/3

Answer 2

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 $a_n$ represents the nth term of the sequence.

now the first term of the sequence is:

$a_1=\dfrac{1}{3}$

second term is:

$a_2=\dfrac{3}{3}$

which could also be obtained as:

$a_2=a_1+\dfrac{2}{3}$

Third term is:

$a_3=\dfrac{5}{3}$

which could also be obtained as:

$a_3=a_2+\dfrac{2}{3}$

Fourth term is:

$a_4=\dfrac{7}{3}$

which could also be obtained as:

$a_4=a_3+\dfrac{2}{3}$

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)