Consecutive Numbers Sum Problem Explained
This problem involves finding four consecutive numbers based on a given condition and then calculating half of their sum.
1. Define the Consecutive Numbers
Let the four consecutive numbers be represented algebraically:
- First number: $n$
- Second number: $n + 1$
- Third number: $n + 2$
- Fourth number: $n + 3$
2. Set Up the Equation from the Condition
The problem states that the sum of the first two numbers equals the fourth number:
$n + (n + 1) = n + 3$
3. Solve for 'n'
Simplify and solve the equation:
- Combine like terms: $2n + 1 = n + 3$
- Subtract $n$ from both sides: $n + 1 = 3$
- Subtract 1 from both sides: $n = 2$
4. Determine the Four Consecutive Numbers
Substitute the value of $n$ back into the expressions for the numbers:
- First number: $n = 2$
- Second number: $n + 1 = 2 + 1 = 3$
- Third number: $n + 2 = 2 + 2 = 4$
- Fourth number: $n + 3 = 2 + 3 = 5$
The four consecutive numbers are 2, 3, 4, and 5.
5. Calculate the Sum of the Four Numbers
Add the four numbers together:
Sum = $2 + 3 + 4 + 5 = 14$
6. Find Half of the Sum
Calculate half of the total sum:
Half of Sum = $14 / 2 = 7$
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Important Questions from Algebric Equations
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
