Answer: The sequence is geometric
Step-by-step explanation:
A geometric sequence is a sequence in which any term after the first term is gotten by multiplication of the previous term by a common ratio , r which is a constant throughout the terms.
While an Arithmetic Progression is a sequence in which any term after the first term is gotten by addition of the previous term by a constant known as the common difference, d.
From this sequence ,400, 480, 576, 691.2, 829.44,
,we can see that the next term is gotten by Multiplication of the previous term by 1.2 .
This was gotten using the formula of common ratio, r which equals
a2/ a= 480/400= 1.2
a3/a2 = 576/ 480= 1.2
a4/a3= 691.2/ 576=1.2
a5/a4= 829.44/ 691.2
The sequence 400, 480, 576, 691.2, 829.44,... is a geometric sequence.
Arithmetic sequence has constant difference between its adjacent terms.
Geometric sequence has each next term obtainable by multiplying previous term with a constant factor.
For this case, we have the sequence as:
400, 480, 576, 691.2, 829.44, ...
Now, let we see if there is constant difference:
480 - 400 = 80
576 - 480 = 96 ≠ 80
So, this sequence is not an arithmetic sequence.
Checking if the sequence has constant factor:
[tex]\dfrac{480}{400} = \dfrac{6}{5} = 1.2[/tex]
[tex]\dfrac{576}{480} = \dfrac{6}{5} = 1.2[/tex]
[tex]\dfrac{691.2}{576} = \dfrac{6}{5} = 1.2[/tex]
[tex]\dfrac{829.44}{691.2} = \dfrac{6}{5} = 1.2[/tex]
So we see that each next term is made by multiplying 1.2 in the previous term. Therefore, each next term obtainable by multiplying previous term with a constant factor.
Thus, the considered sequence is geometric sequence.
Learn more about geometric sequence here:
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