A manufacturer of TV sets produced 6000 units in the third year and 7000 units in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find the production

Question

Philoid · Accepted 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, ........a_{n - 1}, a_n).

Given: -

The 3^rd year production is 6000 units

So,

a₃ = 6000

We know that a_n = a + (n - 1) ×d

a₃ = a + (3 - 1)×d

6000 = a + 2d

The 7^th 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 10^th year = a₁₀ = a + (10 - 1)×d

a₁₀ = 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 = a₁ + a₂ + a₃ + a₄ + a₅ + a₆ + a₇

s₇ = 43750

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

A manufacturer of TV sets produced 6000 units in the third year and 7000 units in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find the production(i) in the first year,(ii) in the 10th year,(iii) in 7 years.

A manufacturer of TV sets produced 6000 units in the third year and 7000 units in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find the production
(i) in the first year,

(ii) in the 10^th year,

(iii) in 7 years.