Answer :

Hint: - In the question it is mentioned that the production increases by a fixed number every year.


So it is an A.P. (a1, a2, a3, a4, ........an - 1, an).


Given: -


The 3rd year production is 6000 units


So,


a3 = 6000


We know that an = a + (n - 1) ×d


a3 = a + (3 - 1)×d


6000 = a + 2d


The 7th year production is 7000 units


So,


a7 = 7000


a7 = a + (7 - 1)×d


7000 = a + 6d


From equations (1)&(2) we get,


6000 - 2d = 7000 - 6d


4×d = 1000


d = 250


From equations (1)&(2) we get,


a = 5500


i. Production in the first year = a = 5500


5500 units were produced by the manufacturer of TV sets in the first year.


ii. Production in the 10th year = a10 = a + (10 - 1)×d


a10 = 5500 + (9) ×250


= 7750


7750 units were produced by the manufacturer of TV sets in the 10th year.


iii. Total production in seven years = a1 + a2 + a3 + a4 + a5 + a6 + a7




s7 = 43750


A total of 16, 250 units was produced by the manufacturer in 7 years.


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