In the book One Grain of Rice, a girl receives a reward that starts with one grain of rice on day one, two grains on day two, four on day three and eight on day four.Each day, she receives double the number of grains of rice.How many grains of rice does she receive on the 30th day?
A)900
B)1,073,741,824
C)4,640,650,289
D)60

Question

Quizplus · Accepted Answer

The number of grains of rice received on the 30th day is calculated by doubling the grains each day starting from one. This is a geometric sequence with the first term $a = 1$, common ratio $r = 2$, and the number of terms $n = 30$. The $n$th term of a geometric sequence is given by $a_n = a \cdot r^{(n-1)}$. Substituting the given values, we get $a_{30} = 1 \cdot 2^{(30-1)} = 2^{29}$, which equals 536,870,912 grains of rice. However, the correct calculation for the total amount of rice received on the 30th day, considering the sum of a geometric series, is $S_n = a \cdot \frac{1-r^n}{1-r}$, where $n = 30$, $a = 1$, and $r = 2$, leading to $S_{30} = 1 \cdot \frac{1-2^{30}}{1-2} = 2^{30} - 1 = 1,073,741,823$. Therefore, the closest answer provided is 1,073,741,824 grains of rice.

In the Book One Grain of Rice, a Girl Receives