Answer:
The equation to find the answer is [tex]9=1+(n-1)2[/tex].
It has been 5 days since Karen has set her watch.
Step-by-step explanation:
Given:
Karen set her watch 1 second behind
So we will consider;
First term 'a' = 1 second
Also Given :
it falls behind another 2 seconds every day.
So we can consider;
Common difference = 2
We need to find number of days it has been 9 seconds since Karen last set her watch
Solution:
Let number of days be represented by 'n'.
Also Let [tex]T(n) = 9[/tex]
Now By Applying formula for Arithmetic Progression we get;
[tex]T(n)=a+(n-1)d[/tex]
Substituting the given values we get;
[tex]9=1+(n-1)2[/tex]
Hence The equation to find the answer is [tex]9=1+(n-1)2[/tex].
On Solving the above equation we get;
Subtracting both side by 1 we get;
[tex]9-1=1+(n-1)2-1\\\\8=(n-1)2[/tex]
Now Dividing both side by 2 we get;
[tex]\frac{8}{2}=\frac{(n-1)2}{2}\\\\4=n-1[/tex]
Adding 1 on both side we get;
[tex]4+1=n-1+1\\\\n=5[/tex]
Hence It has been 5 days since Karen has set her watch.