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Solution


Q.

A road roller, often called a roller compactor or just a roller, is an engineering vehicle used to compact soil, gravel, concrete, or asphalt in the construction of roads and foundations. Similar machines are also used in landfills or agriculture. Past records of a road roller manufacturing company show that the number of products produced forms an arithmetic progression (AP).
The company produced 270 road rollers in the 4th year and 510 in the 10th year.

Based on the above information, answer the following questions

 

(i) What was the company’s production in first year
1 150  
2 140  
3 120  
4 110  

Ans.

(1)

Let a and d be the first term and common difference of the AP formed by the number of products produced by the company every year.

We have:

 a4=270⇒a+3d=270 ...(i)"Also, a10=510⇒a+9d=510...(ii)"Subtracting (i) from (ii): 6d=240⇒d=240/6=40Substituting d=40in (i):a+3×40=270 a=270-120=150Production in first year = 150.