Answer :
The next two numbers of the geometric sequence will be 27 , 81.
Geometric Sequence or Geometric Progression is defined as a sequence where every term is multiplied by a constant fixed number to get the next term except the first term.
For Example ; 2,6,18,54,..... This is a Geometric sequence as every next term except the first term is multiplied with 3.
Geometric Sequence is denoted by [tex]a,ar,ar^{2} ,ar^{3} ,.....[/tex]
Its general term is denoted by [tex]a_{n} =a.r^{n-1}[/tex], where a is the first term
r is the common ratio
n is the number of term in the sequence.
According to the given question
given the first two term = 3,9
So a=3 …..(1)
next we need common ratio "r" for this we divide second term by first term .
that is [tex]\frac{a_{2} }{a_{1} }[/tex].
r=9/3
r=3.
The next term of the sequence will be third and fourth term i.e. [tex]a_{3} ,a_{4}[/tex].
[tex]a_{3} =a*r^{3-1}[/tex] ( using general formula for GP)
Substituting the value as a=3 and r=3
[tex]a_{3} =3^{3} \\ \\ a_{3} =27[/tex]
Now
[tex]a_{4} =a*r^{4-1}[/tex]
Substituting the value as a=3 and r=3
[tex]a_{4} =3*3^{3}[/tex]
[tex]a_{4} =3^{4}\\ \\ a_{4} =81[/tex]
Therefore , The next two numbers of the geometric sequence will be 27 , 81.
learn more about Geometric Sequence here https://brainly.com/question/16549240
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