If the mean of the set of numbers x1,x2,x3,…,xn is x¯ , then the mean of the numbers xi+2i,1≤i≤n is
x+2n
x+n+1
x+2
x+n
We know that x¯=∑i=1n xin⇒∑i=1n xi=nx¯∴∑i=1n xi+2in=∑i=1n xi+2∑i=1n in=nx¯+2(1+2+…n)n=nx¯+2n(n+1)2n=x¯+(n+1)