A boy agrees to work at the rate of one rupee on the first day, two rupees on the second day, and four rupees on third day and so on. How much will the boy get if he started working on the 1st of February and finishes on the 20th of February?

A. 2²⁰

B. 2²⁰ -1

C. 2¹⁹ -1

D. 2¹⁹

E. None of these

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & {1^{st}}\,{\text{term}} = 1; \cr & {\text{Common}}\,{\text{ration}} = 2 \cr & {\text{Sum}}\left( {{S_n}} \right) = a \times \frac{{ {{r^n} - 1} }}{{ {r - 1} }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1 \times \frac{{ {{2^{20}} - 1} }}{{ {2 - 1} }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {2^{20}} - 1 \cr} $$