Respuesta :
Answer:
Explicit formula is 2(5)^(n-1).
Step-by-step explanation:
This is a Geometric Sequence with common ratio 10/2 = 50/10 = 250/50 = 5.
The nth term an = a1 r^(n - 1)
= 2(5)^(n-1).
Formula for sequence tells about getting its specific term by putting its index. The formula for considered sequence is [tex]\{2(5)^{i-1}\}_{i=1}^\infty[/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]d[/tex]
Then the sequence would look like
[tex]a, ad, ad^2, ad^3, ad^4,...[/tex] (till the terms to which it is defined)
Thus, the nth term of such sequence would be
[tex]T_n = ad^{n-1}[/tex]
For the given sequence, it can be seen that each previous term is multiplied by 5 to get the next term to that term.
Like, we got
[tex]10 = 2 \times 5\\50 = 10 \times 5[/tex] and so on.
This shows that there is single constant used which is multiplied to previous terms to get the next term. This is the property of a geometric sequence. Here, we got
[tex]a = 2\\d = 5[/tex]
Thus, sequence is
[tex]a, ad, ad^2, ad^3, ...\\\\or\\\\2, 2\times 5, 2 \times 5^2, 2 \times 5^3 ...\\\\or\\2, 10, 50, 250, 1250,...[/tex]
Its nth term is given as: [tex]T_n = ad^{n-1} = 2(5)^{n-1}[/tex]
A sequence with n terms, and its nth term formula being [tex]a_n[/tex] is written as [tex]\{a_i\}_{i=1}^n[/tex] (showing that put i = 1, 2, ... n) to get its terms.
Here, sequence is not limited, so infinite terms.
or, we get the formula for the sequence as: [tex]\{a_i\}_{i=1}^n = \{2(5)^{i-1}\}_{i=1}^\infty[/tex]
Thus, The formula for considered sequence is [tex]\{2(5)^{i-1}\}_{i=1}^\infty[/tex]
Learn more about geometric sequence here:
https://brainly.com/question/2735005
