A manufacturer of t.v sets produced 600 sets in the third year and 700 sets in the seventh year. Find 1 the production in the first year, 2 the production in the 10th year , 3 the total production in the first 7 year.
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A manufacturer of TV sets produced 600 units in the third year and 700 units in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find the production in
(i) the first year- ( a )
(ii) the 10
th
year- ( b )
(iii) 7 years - ( c )
Find ( c )-( a )-( b )
MEDIUM
ANSWER
Let 'a' be the first term and 'd' be the common difference of the A.P formed
a
3
=a+2d=600.................(i)
And a
7
=a+6d=700......(ii)
Solving equation (i) and (ii)
a=550 and d=5
(i) Production in the first year is 550 TV sets.
(ii) Production in the 10th year = a
10
=a+9d
=550+9(25)
=550+225
=775
(iii) Total production in 7 years =
S
7
=
2
7
[2(550)+(7−1)25]
=4375.
Thus, the total production in 7 years if of 7375 TV sets
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