A manufacturer of the radio sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the product increases uniformly by a fixed number every year, find

(і) the production in the first year

(іі) the total product in the 7 years and

(ііі) the product in the 10^{th} year.

Solution |||

(і) the production in the first year

Answer:

**Given:** 600 and 700 radio sets units are produced in third and seventh year respectively

**To find:** the production in the first year i.e. a

⇒ a_{3} = 600 and a_{7} = 700

**Formula used:**

For an A.P., a_{n} is n^{th} term which is given by,

a_{n} = a + (n – 1)d

where a is first term, d is common difference and n is number of terms in an A.P.

Therefore,

a_{3} = a + (3 – 1)d

⇒ 600 = a + 2d……………………(1)

a_{7} = a + (7 – 1)d

⇒ 700 = a + 6d

⇒ a = 700 – 6d………………………(2)

Now put this value of a in equation (1):

⇒ 600 = 700 – 6d + 2d

⇒ 600 – 700 = – 6d + 2d

⇒ –100 = –4d

⇒ d = 25

Put d = 25 in equation (2):

⇒ a = 700 – 6(25)

⇒ a = 700 – 150

⇒ a = 550

**Production in the first year = a = 550**

(іі) the total product in the 7 years