Let x 1 , x 2 , … , x 100 be in an arithmetic progression, with x 1 = 2 and their mean equal to 200 . If y i = i x i - i , 1 ≤ i ≤ 100 , then the mean of y 1 , y 2 , … , y 100 is

Step-by-step solution

Given, Mean of x 1 ,   x 2 . . . . . . . . . . , x 100 is 200 So, the sum of observation will be, ∑ x i = 100 × 200 Now using the sum of A . P formula in above equation as all terms are in arithmetic progression we get, 100 2 x 1 + x 100 = 100 × 200 ⇒ 50 2 + x 100 = 100 × 200 ⇒ x 100 = 398 ⇒ x 1 + 99 d = 398 ⇒ d = 4 Now, x i = 2 + ( i - 1 ) 4 = 4 i - 2 So, y i = i x i - i = 3 i 2 - 2 i Now finding mean we get, y ¯ = 1 100 ∑ y i ⇒ y ¯ = 1 100 &#