Question

Your elderly neighbor places a bag of rice on your doorstep each morning. The first day, the bag contained 1 grain of rice, the second day it contained 2 grains of rice, 4 grains of rice the third day, and so on. Each grain of rice weighs 0.04 grams. How many grains of rice will be in the bag on the 26th day?

Answer 1

On 26th day there will be 33,554,432 grains in the bag.

Explanation:

Given:

Number of grains in bag

1st day =1 grain

2nd day= 2 grains

3rd day= 4 grains

And so on.......

The numbers
`1,2,4,.........` show that the numbers are in geometric sequence with common ratio
`r=2` as ratio between consecutive terms is
`=2`.

We need to find number of grains in 26th day.

We apply the
`nth` term formula for geometric sequence.

`a_n=a_(1)r^(n-1)`

where
`a_n` represents the nth term,
`a_1` represents the first term and
`r` represents the common ratio.

Plugging values
`a_1=1\ and\ r=2`

∴
`a_(26)=1(2)^(26-1)`

`a_(26)=(2)^(25)`

`a_(26)=33554432`

∴ On 26th day there will be 33,554,432 grains in the bag.