What is the value of `(1xx 2 +2xx 3-3xx 4 +4xx 5 -5 xx 6 +6 xx 7) `?

Options

A. 28
B. 15
C. 20
D. 24

Answer

To solve the expression \(1 \times 2 + 2 \times 3 - 3 \times 4 + 4 \times 5 - 5 \times 6 + 6 \times 7\), we will evaluate each term step by step.

### Step 1: Calculate each multiplication
1. \(1 \times 2 = 2\)
2. \(2 \times 3 = 6\)
3. \(3 \times 4 = 12\)
4. \(4 \times 5 = 20\)
5. \(5 \times 6 = 30\)
6. \(6 \times 7 = 42\)

### Step 2: Substitute the calculated values into the expression
Now we can substitute these values back into the expression:
\[ 2 + 6 - 12 + 20 - 30 + 42 \]

### Step 3: Perform the addition and subtraction from left to right
1. Start with \(2 + 6 = 8\)
2. Next, \(8 - 12 = -4\)
3. Then, \(-4 + 20 = 16\)
4. Next, \(16 - 30 = -14\)
5. Finally, \(-14 + 42 = 28\)

### Final Result
Thus, the value of the expression \(1 \times 2 + 2 \times 3 - 3 \times 4 + 4 \times 5 - 5 \times 6 + 6 \times 7\) is \(28\).