The sum of 5 consecutive even numbers is 100 . What is the first number in this sequence?

To find the first number in the sequence of 5 consecutive even numbers that sum up to 100, let’s denote the first even number as \( x \). The 5 consecutive even numbers can then be expressed as: \( x, x+2, x+4, x+6, x+8 \). Now, we can set up an equation: \[ x + (x+2) + (x+4) + (x+6) + (x+8) = 100 \] This simplifies to: \[ 5x + 20 = 100 \] Subtracting 20 from both sides gives: \[ 5x = 80 \] Dividing both sides by 5 yields: \[ x = 16 \] So, the first number in this sequence is 16. The numbers are: 16, 18, 20, 22, and 24. Voilà! Another fun fact: Even numbers are the bedrock of many mathematical concepts, like even functions in geometry. They help keep things balanced and symmetrical! Moreover, if you're ever solving problems like this, it helps to remember that the average of these numbers can also give you a quick estimate. The average of 5 consecutive even numbers can be found by dividing their total sum by 5. In this case, \( 100 / 5 = 20 \), meaning the middle number is 20, thus making it easy to backtrack to find the first number!