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