Question

A Manufacturer of laptop produced 6000 units in 3rd year and 7000 units in the 7th year. Assuming the production increases uniformly by a fixed number every year, find
(i) the production in the 1st year,
(ii) the production in the 5th year,
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Answer 1

T7= 7000

T3=6000

a+(7-1)d=7000

a+6d=7000 (i)

similarly

a+2d=6000 (ii)

after solving (i) and (ii)

we'll get d=250

and a=500

so The Production in 1st year will be a that is 5500

and The Production in 5th year will be a+4d that is 5500+250*4 that is 6500

Answer:

(i) 5500

(ii) 6500

Answer 2

Let production in 1st year be a units and increase in production (every year) be d units.

Increase in production is constant.

∴ Unit produced every year forms an A.P.

Now, a3 = 6000 ⇒ a + 2d = 6000 ⇒ a = 6000 – 2d …(i)

and a7 = 7000 ⇒ a + 6d = 7000

⇒ (6000 – 2d) + 6d = 7000 [Using (i)]

⇒ 4d = 1000 ⇒ d = 250

Putting d = 250 in (i), we get a = 6000 –2 × 250 = 5500

(i) Production in first year = 5500

(ii) Production in fifth year, a5 = a + 4d = 5500 + 4 × 250 = 6500

(iii) Production in sixth year, a6 = a + 5d = 5500 + 5 × 250 = 6750