To find the three consecutive odd integers whose sum is 45, follow these steps:
1. Define the Variables:
Let's represent the three consecutive odd integers. We can call the first odd integer [tex]\( x \)[/tex].
The next consecutive odd integer would then be [tex]\( x + 2 \)[/tex].
The third consecutive odd integer would be [tex]\( x + 4 \)[/tex].
2. Set Up the Equation:
Since the sum of these three consecutive odd integers is given as 45, we can set up the following equation:
[tex]\[
x + (x + 2) + (x + 4) = 45
\][/tex]
3. Simplify the Equation:
Combine like terms in the equation:
[tex]\[
x + x + 2 + x + 4 = 45
\][/tex]
[tex]\[
3x + 6 = 45
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
To find the value of [tex]\( x \)[/tex], first subtract 6 from both sides of the equation:
[tex]\[
3x + 6 - 6 = 45 - 6
\][/tex]
[tex]\[
3x = 39
\][/tex]
Next, divide both sides by 3:
[tex]\[
x = \frac{39}{3}
\][/tex]
[tex]\[
x = 13
\][/tex]
5. Identify the Three Consecutive Odd Integers:
Now that we have [tex]\( x = 13 \)[/tex], we can determine the three consecutive odd integers:
[tex]\[
\text{First integer: } 13
\][/tex]
[tex]\[
\text{Second integer: } 13 + 2 = 15
\][/tex]
[tex]\[
\text{Third integer: } 13 + 4 = 17
\][/tex]
So, the three consecutive odd integers are 13, 15, and 17.
The second integer in the sequence is [tex]\( 15 \)[/tex].
