# If the variance of the term in an increasing AP b1,b2,b3,...........,b11 is 90 then the common diffrence of this AP is .

Solution:

$\\ Var(x)=\sum bi^2/11-(\sum bi/11)^2\\ \\\Rightarrow 90=[a^2+(a+d)^2+(a+2d)^2+..........+(a+10d)^2]/11\\ \\\Rightarrow [a+a+d+a+2d+..........+(a+10d)]^2\\ \\\Rightarrow 10890=11[11a^2+385d^2+110ad]-[11a+55d]^2\\ \\\Rightarrow 10890=1210d^2\\ \\\Rightarrow d=3$

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