The sum of 10 consecutive integers is 5. What is the lowest integer?

Options

A. a)-1
B. b)-5
C. c)-4
D. d)-3

Answer

To find the lowest integer among 10 consecutive integers whose sum is 5, we can follow these steps:

### Step 1: Define the integers
Let the first integer be \( x \). Then the 10 consecutive integers can be represented as:
- \( x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, x+9 \)

### Step 2: Write the equation for the sum
The sum of these integers can be expressed as:
\[ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) + (x + 7) + (x + 8) + (x + 9) = 5 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 10x + (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 5 \]
The sum of the integers from 0 to 9 is:
\[ 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 \]
So the equation becomes:
\[ 10x + 45 = 5 \]

### Step 4: Solve for \( x \)
Now, isolate \( x \):
\[ 10x = 5 - 45 \]
\[ 10x = -40 \]
\[ x = -4 \]

### Step 5: Identify the lowest integer
Since \( x \) is the first integer, the lowest integer among the 10 consecutive integers is:
\[ \text{Lowest integer} = x = -4 \]

### Final Answer
The lowest integer is \( -4 \).

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