Karen set her watch 1 second behind, and it falls behind another 2 seconds every day. How many days has it been since Karen last set her watch if the watch is 9 seconds behind? Write and solve an equation to find the answer.

Respuesta :

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.