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10th Class Mathematics Arithmetic Progressions Question Bank Arithmetic Progressions

  • question_answer
    A manufacturer of laptop produced 6000 units in 3rd year and 7000 units in the 7th year. Assuming that production increases uniformly by a fixed number every year, find the production in the 5th year.       

    A) 6500 units       

    B) 5000 units       

    C) 6000 units   

    D)  8000 units

    Correct Answer: A

    Solution :

    Since, production of Laptops in 3rd year = 6000 \[\Rightarrow \]  \[{{a}_{3}}=6000\]  \[\Rightarrow \] \[a+2d=6000\]      .... (I) Also production of laptops in 7th year = 7000 \[{{a}_{7}}=7000\Rightarrow a+6d=7000\]              ?.. (ii) Subtracting (i) from (ii), we get \[4d=1000\,\,\,\Rightarrow \,\,\,d=250\] From (i), \[a+2(250)=6000\,\,\,\Rightarrow \,\,\,a=5500\] Hence, production in fifth year \[{{a}_{5}}=a+4d=(5500+4\,(250))=6500\]units


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