Question

write the rule to explain the pattern and find the missing numbers: 5,832; BLANK; 648; 216; 72; BLANK; 8

Answer 1

The missing numbers in the pattern are 1,944 and 24. The pattern is each number is divided by 3 to obtain the next number.

Step-by-step explanation:

To find the missing numbers in the given pattern, we need to identify the rule or pattern. Looking at the sequence of numbers, we can observe that each number is a multiple of 3. Starting with 5,832, each number is divided by 3 to obtain the next number. So, the missing numbers can be found by dividing the previous number by 3.

Using this pattern, we can find the missing numbers:

1. 5,832 ÷ 3 = 1,944
2. 648 ÷ 3 = 216
3. 216 ÷ 3 = 72
4. 72 ÷ 3 = 24
5. 24 ÷ 3 = 8

Therefore, the missing numbers in the pattern are 1,944 and 24.

Answer 2

The sequence is given by:
5832, ...., 648, 216, 72,..., 8, .....
The rule that explains the sequence will be given as follows:
first term=5832
common ratio=216/648=72/216=1/3
given that the sequence has a common ratio, then the sequence is a geometric sequence given by:
an=ar^(n-1)
where:
an=nth term
a=first term
r=common ration
n=number of term
thus the rule will be:
an=5832(1/3)^(n-1)