The sum of the 2 larger integers in terms of a is [tex]\frac{a}{2}[/tex] + 4 ⇒ A
Step-by-step explanation:
The consecutive numbers are the numbers after each other
So:
n , n + 1 , n + 2, ........ are consecutive integers
n, n + 2, n + 4, ........ are consecutive odd/even integers
Assume that the four consecutive numbers are n , n + 2 , n + 4 , n + 6
∵ The sum of 4 consecutive odd integers
∵ The 4 consecutive numbers are n , n + 2 , n + 4 , n + 6
∴ n + n + 2 + n + 4 + n + 6 = a
∴ 4n + 12 = a
- Subtract 12 from both sides
∴ 4n = a - 12
- Divide both sides by 4
∴ [tex]n=\frac{a-12}{4}[/tex]
∵ The two larger numbers are n + 4 and n + 6
∵ Their sum = n + 4 + n + 6
∴ Their sum = 2n + 10
- Substitute n by [tex]\frac{a-12}{4}[/tex]
∴ Their sum = 2( [tex]\frac{a-12}{4}[/tex] ) + 10
∴ Their sum = [tex]\frac{a-12}{2}[/tex] + 10
- Simplify the expressions
∴ Their sum = [tex]\frac{a}{2}[/tex] - 6 + 10
- Add like terms
∴ Their sum = [tex]\frac{a}{2}[/tex] + 4
The sum of the 2 larger integers in terms of a is [tex]\frac{a}{2}[/tex] + 4
Learn more:
You can learn more about the consecutive numbers in brainly.com/question/5496711
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