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 10th 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
⇒ a3 = 600 and a7 = 700
Formula used:
For an A.P., an is nth term which is given by,
an = a + (n – 1)d
where a is first term, d is common difference and n is number of terms in an A.P.
Therefore,
a3 = a + (3 – 1)d
⇒ 600 = a + 2d……………………(1)
a7 = 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
To find: the sum of totals products in 7 years i.e. S7
Formula used:
where a is first term, d is common difference and n is number of terms in an A.P.
Therefore,
⇒ S7 = 7(625)
⇒ S7 = 4375
Hence, the total product in the 7 years are 4375
(ііі) the product in the 10th year
Answer:
To find: the product in the 10th year i.e. a10
Formula used:
For an A.P., an is nth term which is given by,
an = a + (n – 1)d
where a is first term, d is common difference and n is number of terms in an A.P.
Therefore,
a10 = 550 + (10 – 1)25
⇒ a10 = 550 + (9)25
⇒ a10 = 550 + 225
⇒ a10 = 775
Hence, the product in the 10th year are 775 units