700, 1200, 1600, 2000, x
If the mean of the five numbers above is 1600, what is the value of x ?

Explanation

To find the value of \( x \) in the sequence \( 700, 1200, 1600, 2000, x \) given that the mean of these five numbers is \( 1600 \), we can follow these steps:

### Step 1: Write the formula for the mean
The mean (average) of a set of numbers is calculated by dividing the sum of the numbers by the total count of the numbers. For our case, the mean is given by:
\[ \text{Mean} = \frac{\text{Sum of numbers}}{\text{Total count of numbers}} \]
Here, we have 5 numbers, so:
\[ 1600 = \frac{700 + 1200 + 1600 + 2000 + x}{5} \]

### Step 2: Multiply both sides by 5
To eliminate the fraction, multiply both sides of the equation by 5:
\[ 5 \times 1600 = 700 + 1200 + 1600 + 2000 + x \]
This simplifies to:
\[ 8000 = 700 + 1200 + 1600 + 2000 + x \]

### Step 3: Calculate the sum of the known numbers
Now, we need to calculate the sum of the known numbers:
\[ 700 + 1200 + 1600 + 2000 = 4700 \]

### Step 4: Substitute the sum back into the equation
Now, substitute the sum back into the equation:
\[ 8000 = 4700 + x \]

### Step 5: Solve for \( x \)
To find \( x \), subtract \( 4700 \) from both sides:
\[ x = 8000 - 4700 \]
\[ x = 3300 \]

### Final Answer
Thus, the value of \( x \) is \( 3300 \).

---