Sequence of numbers is collection of ordered numbers. The given sequence is described by formula: [tex]\{\dfrac{27}{3^{n-1}}\}^5_1[/tex]
What is a geometric sequence and how to find its nth terms?
There are three parameters which differentiate between which geometric sequence we're talking about.
The first parameter is the initial value of the sequence.
The second parameter is the quantity by which we multiply previous term to get the next term.
The third parameter is the length of the sequence. It can be finite or infinite.
Suppose the initial term of a geometric sequence is [tex]a[/tex] and the term by which we multiply the previous term to get the next term is [tex]r[/tex]
Then the sequence would look like [tex]a, ad, ad^2, ...[/tex]
(till the terms to which it is defined)
Thus, the nth term of such sequence would be
[tex]T_n = ad^{n-2}[/tex]
For the given sequence, it can be seen that each term is divided by 3 to get the next term. We can take it as we're doing multiplication by 1/3
Thus, the given sequence is geometric sequence and its characteristics are:
[tex]n = 5 \text{ (Number of terms)}\\a = 27 \text{(Initial term)}\\d = 1/3 \text{ (Multiplication factor)}[/tex]
Thus, ith term is given as:
[tex]T_i = ad^{i-2} = 27 \times {1/3}^{i-2} = \dfrac{27}{3^{i-2}}[/tex]
We write sequence as: [tex]\{a_n\}_b^c[/tex]
where n starts with value b and runs integer values and end up on n = c
For this case, we've n = 1 to 5, thus,
The given sequence is written as:
[tex]\{\dfrac{27}{3^{n-1}}\}^5_1[/tex]
Thus,
The given sequence is described by formula: [tex]\{\dfrac{27}{3^{n-1}}\}^5_1[/tex]
Learn more about geometric sequence here:
https://brainly.com/question/2735005
