Question

the sum of 5 consecutive odd numbers is 135. what is the second number in this sequence?

Explanation:

Step1: Define the middle odd number

Let the middle (third) consecutive odd number be \( x \). Then the five consecutive odd numbers are \( x - 4 \), \( x - 2 \), \( x \), \( x + 2 \), \( x + 4 \). This is because consecutive odd numbers differ by 2, so the first is 4 less than the middle, the second is 2 less, the fourth is 2 more, and the fifth is 4 more.

Step2: Sum the numbers and solve for \( x \)

The sum of these five numbers is \( (x - 4) + (x - 2) + x + (x + 2) + (x + 4) = 135 \). Simplifying the left side, the \( -4 \) and \( +4 \) cancel, \( -2 \) and \( +2 \) cancel, leaving \( 5x = 135 \). Dividing both sides by 5, we get \( x=\frac{135}{5}=27 \).

Step3: Find the second number

The second number is \( x - 2 \). Substituting \( x = 27 \), we get \( 27 - 2 = 25 \).

Answer:

25