Question

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

• A. $\overline{x}+\frac{3^{n+1}}{n}$
• B. $\overline{x}+3\left(\frac{3^n-1}{2n}\right)$
• C. $\overline{x}+\frac{3^n}{n}$
• D. $\overline{x}+3\left(\frac{3^{n-1}-1}{2n}\right)$

Answer 1

The correct option is B $\overline{x}+3\left(\frac{3^n-1}{2n}\right)$

new mean $=\frac{x_1+x_2+...+x_n}{n}+\frac{3+3^2+...+3^n}{n}=\overline{x}+3\left(\frac{3^n-1}{2n}\right)$