A TV manufacturer has produced 1000 TVs in the seventh year and 1450 TVs in the tenth year. Assuming that the production increases uniformly by a fixed number every year, find the number of TVs produced in the first year and in the 15th year.

Here, t₇ = 1000 and t₁₀ = 1450

We know that nth term of A.P. , t_n = a + (n – 1) d.

First, t₇ = a + (7 – 1) d = 1000

⇒ a + 6d = 1000 … (1)

Then, t₁₀ = a + (10 – 1) d = 1450

⇒ a + 9d = 1450 … (2)

From (1) and (2),

a + 6d = 1000

a + 9d = 1450

(-) (-) (-)

-3d = -450

⇒ d = 450/3 = 150

Substituting d = 150 in (1),

⇒ a + 6(150) = 1000

⇒ a = 1000 – 900 = 100

Now, t₁ = 100 + (1 – 1) (150)

= 100 + 0

= 100

And t₁₅ = 100 + (15 – 1) (150)

= 100 + 14 (150)

= 100 + 2100

= 2200

∴ Number of TVs produced in the first year are 100 and in the 15^th year are 2200.