Let $x_1,x_2,x_3,\ldots,x_{20}$ be in geometric progression with $x_1=3$ and the common ratio $\frac{1}{2}$. A new data is constructed replacing each $x_i$ by $(x_i-i)^2$. If $\bar{x}$ is the mean of new data, then the greatest integer less than or equal to $\bar{x}$ is __________.

JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 28 July 2022, Shift 1, Maths Q28

Question 28 of 90 in this shift, Maths question 28 of 30, Section B.

Let

x_1,x_2,x_3,\ldots,x_{20}

be in geometric progression with

x_1=3

and the common ratio

\frac{1}{2}

. A new data is constructed replacing each

x_i

(x_i-i)^2

. If

\bar{x}

is the mean of new data, then the greatest integer less than or equal to

\bar{x}

is __________.

Official answer

142

NTA final key (2022 Session 2).