Answer :

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

So it is an A.P. (a_{1}, a_{2}, a_{3}, a_{4}, ........a_{n - 1}, a_{n}).

Given: -

The 3^{rd} year production is 6000 units

So,

a_{3} = 6000

We know that a_{n} = a + (n - 1) ×d

a_{3} = a + (3 - 1)×d

6000 = a + 2d

The 7^{th} year production is 7000 units

So,

a_{7} = 7000

a_{7} = 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 10^{th} year = a_{10} = a + (10 - 1)×d

a_{10} = 5500 + (9) ×250

= 7750

∴7750 units were produced by the manufacturer of TV sets in the 10^{th} year.

iii. Total production in seven years = a_{1} + a_{2} + a_{3} + a_{4} + a_{5} + a_{6} + a_{7}

s_{7} = 43750

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

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