The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. Find the production during (i) first year (ii) 8th year (iii) first 6 years.

The production of TV sets in a factory increases uniformly by a fixed

1.	The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. Find the production during (i) first year (ii) 8th year (iii) first 6 years.
Answer» Let the production during first year be a and let d be the increase in production every year. Then, `T_(6) = 16000 rArr a +5d = 16000 " "…(i)` `"and" T_(9) = 22600 rArr a + 8d = 22600 " "...(ii)` On subtracting (i) from (ii), we get `3d = 6600 rArr d = 2200` Putting d = 2200 in (i), we get `a + 5 xx 2200 = 16000 rArr a + 11000 = 16000` ` rArr a = 16000 -11000 = 5000` Thus, a = 5000 and d = 2200. (i) Production during first year, a = 5000 (ii) Production during 8th year is given by `T_(8) = (a +7d) = (5000 + 7 xx 2200) = (5000 + 15400) = 20400.` (iii) Production during first 6 years is given by `S_(6) = (6)/(2) {2a+5d} = 3(2 xx 5000 + 5 xx 2200)` ` = 3(10000 + 11000) = 63000`