Question

If the first terms of geometric sequence are 3 and 9 what could be the next two numbers

Answer 1

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 $a,ar,ar^{2} ,ar^{3} ,.....$

Its general term is denoted by $a_{n} =a.r^{n-1}$, 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 $\frac{a_{2} }{a_{1} }$.

r=9/3

r=3.

The next term of the sequence will be third and fourth term i.e. $a_{3} ,a_{4}$.

$a_{3} =a*r^{3-1}$       ( using general formula for GP)

Substituting the value as a=3 and r=3

$a_{3} =3^{3} \\ \\ a_{3} =27$

Now

$a_{4} =a*r^{4-1}$

Substituting the value as a=3 and r=3

$a_{4} =3*3^{3}$

$a_{4} =3^{4}\\ \\ a_{4} =81$

Therefore , The next two numbers of the geometric sequence will be 27 , 81.

learn more about Geometric Sequence here brainly.com/question/16549240

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