A manufacture of TV sets produced 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year, find
(i) the production in the first year
(ii) the production in the 10th year
(iii) the total production in 7 years
(i) the production in the first year
(ii) the production in the 10th year
(iii) the total production in 7 years
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Let the number of sets produced in 1st year be 'a' and 'd' be the increase in production every year.We are given,a+2d= 600 ----- (1)
anda+6d= 700 ----- (2)
subtracting equation (1) from (2), we get
4d= 100 ord= 25
Substituting d=25 in equation (1), we get
a= 550
(a) Production in the first year =a= 550
(b) Production in 10th year = a+ 9d = 550+9 x25 =775
(c) Total production in first 7 years = a+ (a+d)+(a+2d)+.....+(a+6d)
7/2
(2*550 +(7-1)25)
4375