Answer :

Ok

We have our data:

[tex]17;\text{ 187; 2057; 22627}[/tex]

We first find the ratio (r), and that we do dividing one of the values for the inmediatly lower value:

[tex]r=\frac{187}{17}\Rightarrow r=11[/tex]

And we doublecheck it by doing the same with other values:

[tex]r=\frac{2057}{187}\Rightarrow r=11[/tex]

Now that we have the ratio (r), we the add the first term (a):

[tex]a=17[/tex]

So, by definition the geometric sequence will be going as follows:

[tex]a_n=a\cdot r^{n-1}[/tex]

Where a_n will be the geometric sequence, a the first term, r the ratio and n the ammount of terms, so:

[tex]a_n=(17)(11)^{n-1}[/tex]

Now if you want to find the 3rd value in the sequence, you just replace n and so on:

[tex]a_3=(17)(11)^{3-1}\Rightarrow a_3=2057[/tex]

And the fourth:

[tex]a_4=(17)(11)^{4-1}\Rightarrow a_4=22627[/tex]

Therefore, the geometric sequence is:

[tex]a_n=(17)(11)^{n-1}[/tex]

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Rewritten by : Barada