a factory produced 1100 cars in the third year and 2700 cars in the 11th year assuming that the production increases by a fixed number every year,find the production of cars in the 20th year and total cars produced in first 20years

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since the production increases by a fixed no therefore the production is in AP

production of car in 3rd year=

a+2d=1100  (1)

production of car in 11th year=

a+10d=2700  (2)

subtracting (1) from (2) we get

a+10d-(a+2d)=2700-1100

a+10d-a-2d=1600

8d=1600

d=200

substituing the value od d in equation(1) we get

a+2(200)=1100

a+400=1100

a=1100-400

a=700

production of car in 20th year=

a+19d=a20

700+3800=a20

a20=4500

so the production of car in 20th year is 4500

total car produced in 20 years=

n/2(2a+(n-1)d)=sn

s20=20/2{2(700)+19(200)}

s20=10{1400+3800}

s20=10(4200)

s20=42000

therefore 42000 cars will be produced in 20years

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