Introduction to the Expression
The expression 4, 3, 12, 30, 144, 5040 is a sequence of numbers that follow a distinct pattern. In order to find the relationship between these numbers, we will evaluate the expression step by step and explore the mathematics behind them.
Step 1: Finding the Pattern
To evaluate the expression, we first need to identify the pattern that governs the sequence of numbers. By examining the numbers closely, we can observe that each subsequent number is obtained by multiplying the previous number by a specific factor. Let’s break it down:
- 4 x 3 = 12
- 12 x 2.5 = 30
- 30 x 4.8 = 144
- 144 x 35 = 5040
From the calculations above, we can deduce that each number in the sequence is obtained by multiplying the previous number by a specific factor. This factor seems to increase gradually, leading to a significant jump in the final result.
Step 2: Calculating the Missing Factor
In order to evaluate the expression, we need to determine the exact factor by which each number is multiplied to obtain the next number. Let’s calculate the missing factors:
- 12 ÷ 4 = 3
- 30 ÷ 12 = 2.5
- 144 ÷ 30 = 4.8
- 5040 ÷ 144 = 35
By calculating the missing factors, we can see that the pattern involves multiplying the previous number by an increasing factor of 3, 2.5, 4.8, and 35 respectively to obtain the subsequent numbers in the sequence.
Step 3: Evaluating the Expression
Now that we have identified the pattern and calculated the missing factors, we can evaluate the entire expression 4, 3, 12, 30, 144, 5040 by continuing the sequence based on the pattern we have discovered:
- 5040 x 1.2 = 6048
- 6048 x 1.5 = 9072
- 9072 x 1.8 = 16330.4
- 16330.4 x 2.3 = 37559.92
By applying the pattern we identified earlier, we have successfully evaluated the expression up to the next four numbers in the sequence. The sequence continues to grow exponentially as each number is multiplied by an increasing factor.
Conclusion
In conclusion, the expression 4, 3, 12, 30, 144, 5040 follows a distinct pattern where each number is obtained by multiplying the previous number by a specific factor. By analyzing the pattern and calculating the missing factors, we were able to evaluate the expression and extend the sequence further. This exercise not only demonstrates basic arithmetic principles but also highlights the beauty of mathematical patterns and sequences.
