The sum of 6 consecutive even numbers is 126 . What is the fourth number in this sequence?

To solve for the fourth number in the sequence, let's denote the first even number as \( x \). The 6 consecutive even numbers can be expressed as \( x, x+2, x+4, x+6, x+8, x+10 \). The sum can be set up as: \[ x + (x+2) + (x+4) + (x+6) + (x+8) + (x+10) = 126 \] Combining like terms gives: \[ 6x + 30 = 126 \] Subtracting 30 from both sides leads to: \[ 6x = 96 \] Dividing by 6 results in: \[ x = 16 \] Now we can identify the consecutive even numbers: 16, 18, 20, 22, 24, and 26. Therefore, the fourth number in this sequence is: \[ \text{Fourth number} = 22 \] 22 is the answer! Now, let’s connect some engaging dots about even numbers. Consecutive even numbers can often be seen in patterns across various cultures and traditions, like pairs of socks or bicycle wheels, where balancing is key. Interestingly, did you know that in the realm of number theory, even numbers are highly significant? They’re the backbone of many mathematical calculations, including geometry and algebra. Moreover, when you enter the world of even-numbered games, they're often perceived favorably. For instance, even-numbered seating in theaters can create perfectly balanced performances, ensuring that no vantage point overpowers another. So, whether it's about math or life, it seems being ‘even’ keeps things smooth and stable!