Question

Perform the following tasks:

Simplify the ratio 4 : 22 : 30
Complete the pattern: {486, 162, 54, 18, ___}

Answer 1

1. We may simplify the given extended ratio by dividing the numbers with their GCF. The GCF of the given is 2. Thus, the simplified form is,
                             2: 11: 15
2. The given sequence is a geometric sequence with a common ratio of 1/3. Therefore, following the number 18 is number 6. 

Answer 2

Answer:

1. Simplify the ratio 4 : 22 : 30

Dividing by 2;

2 : 11 : 15

2. Complete the pattern: {486, 162, 54, 18, ___}

We can solve this easily by starting from 18.

First lets check the relation between 18 and 54. Its $18\times3=54$

We have found a relation between the two numbers. Lets check if this works for another numbers.

$54\times3=162$

So, we can say that the series is decreasing by 3 times.

So, the missing number will be : 6

{486, 162, 54, 18, 6}