# There are eight consecutive positive even numbers. The average of the square of the first and the last number is 778. Find the largest number.

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There are eight consecutive positive even numbers. The average of the square of the first and the last number is 778. Find the largest number.

1. 34
2. 30
3. 28
4. 25
5. None of these

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Correct Answer - Option 1 : 34

Given

Average of the square of the first and the last consecutive positive even number = 778

Formula Used

Average = Sum of observation/No. of observation

Calculation

Let the eight consecutive positive even numbers are x, x + 2, x + 4, x + 6, x + 8, x + 10, x + 12, x + 14

So according to question

The average of the square of the first and the last number = 778

⇒ [x2 + (x + 14)2]/2 = 778

⇒ x2 + (x + 14)2 = 1556

⇒ 2x2 + 196 + 28x = 1556

⇒ 2x2 + 28x = 1556 - 196

⇒ x2 + 14 x = 680

⇒ x2 + 14 x – 680 = 0

⇒ x(x + 34) - 20(x + 34) = 0

⇒ (x + 34) (x - 20) = 0

⇒ x = - 34, 20

⇒ x = 20 (- 34 is a negative number)

So the largest positive number will be = x + 14 = 20 + 14 = 34

∴ The largest positive number is 34