A geometric sequence is characterized by its common ratio. The pattern of the given sequence is [tex]13(3)^{n-1}[/tex]
First, we determine if the sequence is geometric or arithmetic.
A geometric has a common ratio (r), and it is calculated as follows:
[tex]r = T_2 \div T_1[/tex] ---- divide 2nd term by the 1st
[tex]r = T_3 \div T_2[/tex] ---- divide 3rd term by the 2nd
So, we have:
[tex]r = 39 \div 13 =3[/tex]
[tex]r = 117 \div 39 =3[/tex]
Both calculated values of r are equal. So, the sequence is geometric.
The pattern is then calculated using geometric nth term formula as:
[tex]T_n = ar^{n-1}[/tex]
Where:
[tex]a = 13[/tex] --- the first term
[tex]r =3[/tex] --- the common ratio
So, we have:
[tex]T_n = ar^{n-1}[/tex]
[tex]T_n = 13 \times 3^{n-1}[/tex]
[tex]T_n = 13(3)^{n-1}[/tex]
Hence, the pattern of the sequence is: [tex]13(3)^{n-1}[/tex]
Read more about geometric pattern at:
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