Question

6 consecutive even integers have a sum of 5,154. Find the 6 even integers

Answer 1

GiveN:-

6 consecutive even integers have a sum of 5,154.

To FinD:-

The 6 even integers.

SolutioN:-

Let the 6 even integers be x, (x + 2), (x + 4), (x + 6), (x + 8), (x + 10).

According to the question,

=> x + (x + 2) + (x + 4) + (x + 6) + (x + 8) + (x + 10) = 5154

=> x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 = 5154

=> 6x + 30 = 5154

=> 6x = 5154 - 30

=> x = 5124/6

• => x = 854.

The numbers are:-

1. x = 854
2. (x + 2) = 854 + 2 = 856
3. (x + 4) = 854 + 4 = 858
4. (x + 6) = 854 + 6 = 860
5. (x + 8) = 854 + 8 = 862
6. (x + 10) = 854 + 10 = 864

VerificatioN:-

=> 854 + 856 + 858 + 860 + 862 + 864 = 5154

=> 5154 = 5154

• => LHS = RHS

Hence verified ✔.

The even integers are 854, 856, 858, 860, 862, 864.