Question

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.

Answer 1

Answer:

The equation to find the answer is  $9=1+(n-1)2$.

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 $T(n) = 9$

Now By Applying formula for Arithmetic Progression we get;

$T(n)=a+(n-1)d$

Substituting the given values we get;

$9=1+(n-1)2$

Hence The equation to find the answer is  $9=1+(n-1)2$.

On Solving the above equation we get;

Subtracting both side by 1 we get;

$9-1=1+(n-1)2-1\\\\8=(n-1)2$

Now Dividing both side by 2 we get;

$\frac{8}{2}=\frac{(n-1)2}{2}\\\\4=n-1$

Adding 1 on both side we get;

$4+1=n-1+1\\\\n=5$

Hence It has been 5 days since Karen has set her watch.