Question

A manufacturer of TV sets produces 600 units in the third year and 700 units in the 7^th year. Assuming that the production increases uniformly by a fixed number every year, find:

1. the production in the first year.
2. the production in the 10^th year.
3. the total production in 7 years.

Answer 1

Since the production increases uniformly by a fixed number every year, the sequence formed by the production in different years in an A.P.

Let the production in the first year = a

Common difference = number of units by which the production increases  every year = d

We have, 

t₃ = 600

`\implies` a + 2d = 600  ...(1)

t₇ = 700

`\implies` a + 6d = 700   ...(2)

Subtracting (1) from (2), we get 

4d = 100

`\implies` d = 25

`\implies` a + 2 × 25 = 600

`\implies` a = 550

i. The production in the first year = 550 Tv sets

ii. The production in the 10^th year = t₁₀

= 550 + 9 × 25

= 775 Tv sets

iii. The total production in 7 years = S₇

= `7/2[2 xx 550 + 6 xx 25]`

= `7/2 [1100 + 150]`

= `7/2 xx 1250`

= 4375 Tv sets