Solution : [tex]F(n)= (320) 1.25^{n-1}[/tex]
In Maths, Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern. Also, learn arithmetic progression here. The common ratio multiplied here to each term to get the next term is a non-zero number. An example of a Geometric sequence is 2, 4, 8, 16, 32, 64, …, where the common ratio is 2.
A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) to the preceding term. It is represented by:
a, ar, ar2, ar3, ar4, and so on.
Where a is the first term and r is the common ratio.
Note: It is to be noted that when we divide any succeeding term from its preceding term, then we get the value equal to the common ratio.
Suppose we divide the 3rd term by the 2nd term we get:
ar2/ar = r
In the same way:
ar3/ar2 = r
ar4/ar3 = r
General Form of Geometric Progression
The general form of Geometric Progression is:
a, ar, ar2, ar3, ar4,…, arn-1
Where,
a = First term
r = common ratio
ar^(n-1) = nth term
On first day , the video was viewed = 320 times .
the number of views was 25% more than the day before which mean increasing 1.25 per day .
G.P.
Where common ratio r = 1.25
First term = f(1) = 320
Formula of nth term in G.P. =
[tex]F(n)= f(1) r^{n-1}[/tex]
So, nth term of the given situation :
[tex]F(n)= (320) 1.25^{n-1}[/tex]
Where f(n) denotes the number of views on nth day .
[tex]F(n)= (320) 1.25^{n-1}[/tex]
So, the number of views Vera's video got on the nth day =
[tex]F(n)= (320) 1.25^{n-1}[/tex]
More details : brainly.com/question/12213438
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