Question

what is the value of the missing number in this sequence? 4, 12, 36, ___, 324, 972, 2916

Answer 1

12÷4=3 and 36÷12=3
so the ratio is same
therefore it is a geometry sequence
$ar ^{n - 1}$
$4 \times 3^{4 - 1}$
=108

Answer 2

The fourth term of the given geometric sequence is 108.

What is geometric sequence?

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio.

What is the formula for finding the nth term of the geometric sequence?

The nth term of the geometric sequence is given by

$a_{n} = ar^{n-1}$

Where,

a is the first term.

r is the common ratio.

n is the nth term.

According to the given question.

We have a sequence.

4, 12, 36, ...

Also, the first term is 4 i.e. a = 4.

Since,

$\frac{12}{4} =3$

$\frac{36}{12} =3$

Here, the common ratio of the given sequence is 3.

Therefore, the given sequence is geometric sequence.

In the given sequence the fourth term is missing.

Therefore, the fourth term of the given geometric sequence is given by

$a_{4} = 4(3)^{4-1}$

⇒$a_{4} = 4(3)^{3}$

⇒$a_{4} =4(27)$

⇒$a_{4} =108$

Hence, the fourth term of the given geometric sequence is 108.

Find out more information about geometric sequence here:

https://brainly.com/question/11266123

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