Question

The mean of $n$ items is $\overline{x}$. If each item is successively increased by $5,5^2,5^3.........,5^n,$ then new mean equals to

• A. $\overline{x}+\frac{5(5^n-1)}{2n}$
• B. $\overline{x}+\frac{5^{n+1}}{n}$
• C. $\overline{x}+\frac{5(5^n-1)}{4n}$
• D. $\overline{x}+\frac{(5^n-1)}{8n}$

Answer 1

The correct option is C $\overline{x}+\frac{5(5^n-1)}{4n}$

From the equation, $\frac{x_1+x_2+......+x_n}{n}=\overline{x}$
$\frac{x_1+5+x_2+5^2+......+x_n+5^n}{n}$
$=\frac{x_1+x_2+.....+x_n}{n}+\frac{5+5^2+.....+5^n}{n}$
$\overline{x}+\frac{5(5^n-1)}{4n}$