Answer:
On 26th day there will be 33,554,432 grains in the bag.
Step-by-step explanation:
Given:
Number of grains in bag
1st day =1 grain
2nd day= 2 grains
3rd day= 4 grains
And so on.......
The numbers [tex]1,2,4,.........[/tex] show that the numbers are in geometric sequence with common ratio [tex]r=2[/tex] as ratio between consecutive terms is [tex]=2[/tex].
We need to find number of grains in 26th day.
We apply the [tex]nth[/tex] term formula for geometric sequence.
[tex]a_n=a_{1}r^{n-1}[/tex]
where [tex]a_n[/tex] represents the nth term, [tex]a_1[/tex] represents the first term and [tex]r[/tex] represents the common ratio.
Plugging values [tex]a_1=1\ and\ r=2[/tex]
∴ [tex]a_{26}=1(2)^{26-1}[/tex]
[tex]a_{26}=(2)^{25}[/tex]
[tex]a_{26}=33554432[/tex]
∴ On 26th day there will be 33,554,432 grains in the bag.
