Respuesta :

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Every next term appears to be three times the previous term, so the sequence is defined recursively by

[tex]a_n=3a_{n-1}[/tex]

and explicitly by

[tex]a_n=3a_{n-1}=3^2a_{n-2}=\cdots=3^{n-1}a_1[/tex]

Given that [tex]a_1=2[/tex], you have

[tex]a_n=2\times3^{n-1}\implies a_{15}=2\times3^{14}=9565938[/tex]

Answer:

[tex]a_{15} = 2(3)^{14}[/tex]

Step-by-step explanation:

the sequence 2, 6, 18, 54, ...,

3 is multiplied with first term to get 6

2*3 = 6

6* 3= 18

18 * 3= 54

Each term is multiplied with 3 to get next term

Given sequence is geometric

To get nth term we use formula

[tex]a_n = a_1(r)^{n-1}[/tex]

Where 'a1' is the first term

r is the common ratio

n is the number of terms

first term a1= 2

Each term is multiplied with 3 to get next term, so r= 3

now we need to find out the fifteenth term so n= 15

[tex]a_{15} = 2(3)^{15-1}[/tex]

[tex]a_{15} = 2(3)^{14}[/tex]

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