Question

A company, which is making 200 mobile phones each week, plans to increase its production. The number of mobile phones produces is to be increased by 20 each week from 200 in week 1 to 220 in week 2, to 240 in week 3 and so on, until it is producing 600 in week N. Find the value of N. The company then plans to continue to make 600 mobile phones each week. Find the total number of mobile phones that will be made in the first 52 weeks starting from and including week 1.

Answer 1

a=200,a+d=20,a+2d=240.......an=600
d=20
n=(an-a)/d+1
n=(600-200)/20+1
n=400/20+1
n=21
an=a+n-1×d
an=200+(52-1)52
an=200+51×52
an=200+2652
an=2852

Answer 2

Answer:

Value of N is 21

The total number of mobile phones that will be made in the first 52 weeks starting from and including week 1 is 1220.

Step-by-step explanation:

We are given that A company, which is making 200 mobile phones each week, plans to increase its production. The number of mobile phones produces is to be increased by 20 each week from 200 in week 1 to 220 in week 2, to 240 in week 3 and so on, until it is producing 600 in week N.

So, It is forming an A.P.

200,220,240, ........., 600

So, first term a = 200

Common difference = d = 220-200 = 240-220=20

Formula of nth term = $a_n=a+(n-1)d$

$600=200+(n-1)20$

$600=200+20n-20$

$600=180+20n$

$420=20n$

$21=n$

Thus the value of N is 21

Now we are supposed to find number of mobile phones that will be made in the first 52 weeks starting from and including week 1.

So,  $a_n=200+(52-1)20$

$a_n=1220$

Thus  the total number of mobile phones that will be made in the first 52 weeks starting from and including week 1 is 1220.