A certain number of people contributed to a charity. The first person contributed one rupee. The rule for contribution was that the next person would contribute double the amount already raised. If the total money raised for the charity was 2187 rupees, then the number of people who contributed to the charity is

Name: A certain number of people contributed to a charity. The first person contributed one rupee. The rule for contribution was that the next person would contribute double the amount already raised. If the total money raised for the charity was 2187 rupees, then the number of people who contributed to the charity is
Uploaded: 2026-05-20T10:45:47.674822+05:30
Duration: 4 min 57 s
Description: A certain number of people contributed to a charity. The first person contributed one rupee. The rule for contribution was that the next person would contribute double the amount already raised. If the total money raised for the charity was 2187 rupees, then the number of people who contributed to the charity is

Solution

Let cumulative total after $$n$$ persons be $$T_n$$. Given $$T_1 = 1$$ and each new person contributes $$2T_{n-1}$$, so $$T_n = T_{n-1} + 2T_{n-1} = 3T_{n-1}$$, i.e., $$T_n = 3^{n-1}$$.

$$3^{n-1} = 2187 = 3^7 \Rightarrow n = 8$$.