The sum of 6 consecutive integers is 519. What is the third number in this sequence?

Solution:

Given, the sum of 6 consecutive integers = 519.

Let the consecutive numbers be x, x + 1, x + 2, x + 3, x + 4 and x + 5.

So, x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 519

⇒ 6x + 15 = 519

⇒ 6x = 519 - 15

⇒ 6x = 504

⇒ x = 504/6

⇒ x = 84

Now, x + 1 = 84 + 1 = 85

x + 2 = 84 + 2 = 86

x + 3 = 84 + 3 = 87

x + 4 = 84 + 4 = 88

x + 5 = 84 + 5 = 89

The 6 consecutive integers are 84, 85, 86, 87, 88 and 89.

Therefore, the third number is 86.

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The sum of 6 consecutive integers is 519. What is the third number in this sequence?

Summary:

The sum of 6 consecutive integers is 519. The third number in this sequence is 86.