After being set up a company manufactures 6000 scooters

Asked by admin @ 23/08/2021 in Math viewed by 307 People

After being set up, a company manufactured 6000 scooters in the third year and 7000 scooters in the seventh year. assuming that the production increases uniformly by a fixed number every year, what is the production in the tenth year?

Answered by admin @ 23/08/2021

Answer:

The production in the tenth year is 7750

Step-by-step explanation:

A company manufactured 6000 scooters in the third year and 7000 scooters in the seventh year.

Since we are given that the production increases uniformly by a fixed number every year

So, It forms an AP

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

So, $a_3=6000$

$a_3=a+(3-1)d=6000$

$a_3=a+2d=6000$ ---A

And $a_7=7000$

$a_7=a+(7-1)d=7000$

$a_7=a+6d=7000$ ---B

Subtract A from B

$a+6d-a-2d=7000-6000$

$4d=1000$

$d=\frac{1000}{4}$

$d=250$

Substitute the value of d in A

$a+2(250)=6000$

$a+500=6000$

$a=5500$

Now to find the production in the tenth year

Substitute n 10 in 1

$a_{10}=5500+(10-1)(250)$

$a_{10}=7750$

Hence the production in the tenth year is 7750

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