Question
The sum of 5 consecutive even numbers is 200. What is the fifth number in this sequence?
Ask by Mathis Schneider. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The fifth number is 44.
Solution
Let the five consecutive even numbers be represented as x, x + 2, x + 4, x + 6, and x + 8. Their sum is given by:
x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 200
Simplify the equation:
5x + 20 = 200
Subtract 20 from both sides:
5x = 180
Divide both sides by 5:
x = 36
Since x is the first number, the fifth number is:
36 + 8 = 44
Thus, the fifth number in the sequence is 44.
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Simplify this solution Extra Insights
Let the five consecutive even numbers be represented as \(x\), \(x+2\), \(x+4\), \(x+6\), and \(x+8\). The sum of these numbers can be expressed as: \[ x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 5x + 20 \] Setting this equal to 200 gives us the equation: \[ 5x + 20 = 200 \] Subtracting 20 from both sides results in: \[ 5x = 180 \] Dividing both sides by 5, we find: \[ x = 36 \] Thus, the five consecutive even numbers are 36, 38, 40, 42, and 44. Therefore, the fifth number in this sequence is: \[ \boxed{44} \]
