Inductive reasoning please determine the next three numbers in patern 15,5,5/3, 5/9, , , ,
Each number is divided by 3.
(5/9) / 3
(5/9) * (1/3) = 5/27
I'm sure you can figure out the next two numbers.
5/36,5/45
To determine the next three numbers in the given pattern using inductive reasoning, we need to look for a common pattern or relationship between the numbers.
Let's examine the given sequence: 15, 5, 5/3, 5/9.
If we observe closely, we can see that each number in the sequence is obtained by dividing the previous number by a specific factor.
To find that factor, we can divide consecutive numbers in the sequence and look for a consistent value.
15 ÷ 5 = 3
5 ÷ (5/3) = 3
(5/3) ÷ (5/9) = 3
We notice that each division gives us the same result, which is 3. So, it seems that the factor between each pair of numbers is 3.
Now, let's continue the pattern by applying the factor of 3 to the last number in the sequence.
(5/9) × 3 = 5/3
(5/3) × 3 = 5
5 × 3 = 15
Therefore, the next three numbers in the pattern are 5/3, 5, and 15.
Final sequence: 15, 5, 5/3, 5/9, 5/3, 5, 15