Answer:
10, 12, 14, 16
Step-by-step explanation:
Given: Four consecutive even integers such that seven times the first exceeds their sum by 18.
Lets assume the first number be "x".
As it is even integers
∴ Second consecutive number will be ![(x+2)](https://tex.z-dn.net/?f=%28x%2B2%29)
Third consecutive number will be ![(x+4)](https://tex.z-dn.net/?f=%28x%2B4%29)
Fourth consecutive number will be ![(x+6)](https://tex.z-dn.net/?f=%28x%2B6%29)
Now, as given seven times the first exceeds their sum by 18.
∴ ![[x+(x+2)+(x+4)+(x+6)]+18 = 7x](https://tex.z-dn.net/?f=%5Bx%2B%28x%2B2%29%2B%28x%2B4%29%2B%28x%2B6%29%5D%2B18%20%3D%207x)
solving the equation to find the number.
⇒ ![[x+(x+2)+(x+4)+(x+6)]+18 = 7x](https://tex.z-dn.net/?f=%5Bx%2B%28x%2B2%29%2B%28x%2B4%29%2B%28x%2B6%29%5D%2B18%20%3D%207x)
Opening parenthesis
![x+x+2+x+4+x+6+18 = 7x](https://tex.z-dn.net/?f=x%2Bx%2B2%2Bx%2B4%2Bx%2B6%2B18%20%3D%207x)
⇒ ![4x+30= 7x](https://tex.z-dn.net/?f=4x%2B30%3D%207x)
subtracting both side by 4x
⇒ ![30= 3x](https://tex.z-dn.net/?f=30%3D%203x)
Dividing both side by 3
∴ x= 10.
Hence, subtituting the value x to find four consecutive even integers.
First number is 10
Second consecutive number will be
= 12
Third consecutive number will be
= 14
Fourth consecutive number will be
= 16
∴ Four consecutive even integers are 10,12,14,16.