Question

Example-15, A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the
seventh year. Assuming that the production increases uniformly by a fixed number every year,
find:
els (
(11)
the production in the 1st year
the total production in first 7 years
the production in the 10th year​

Answer 1

Answer:

Step-by-step explanation:

The production of sets are in an Arithmetic progression as it is increased uniformly every year.

So, in an AP, a= Production in the first year,

d= uniform difference between the succeeding year's production and previous year's production

n= year

Production in the 3rd year = a₃= 600

Production in the 7th year = a₇= 700

(i) Production in the first year = a

a₃ = a+(n-1) d

600 = a+(6-1)d

600= a+5d ⇒ equation 1.

a₇= a+(7-1)d

700= a+6d ⇒ equation 2.

Subtracting equation 1. from 2, We get,

100= d

a= 700-6d= 700-6(100) = 700-100

⇒a=100

(ii) Total production in the 7th year= S₇

Sₙ= n/2 [2a +(n-1)d]

S₇ = 7/2 [2(100) +(7-1)100]

    = 7/2 [200 +600]

    = 7/2 (800)

    = 7(400)

S₇= 2800

(iii) Production in the 10th year = a₁₀

a₁₀= 100+ (10-1)100

   = 100+ 900

a₁₀= 1000