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10th Class Mathematics Arithmetic Progressions Question Bank Arithmetic Progressions

  • question_answer
    There are 25 trees at equal distances of 5 metres in a line with a well, the distance of the well from the nearest tree being 10 metres. A gardener waters all the trees separately starting from the well and he returns to the well after watering each tree to get water for the next. Find the total distance the gardner will cover in order to water all the trees.

    A) 3000 m           

    B) 3500 m           

    C) 3800 m       

    D)         4000 m          

    Correct Answer: B

    Solution :

    Since, distance of nearest tree from the well = 10 m Also, each tree is at equal distance of 5 m from the next tree. \[\therefore \] A.P. formed is 10, 15, 20, ........... Here, \[a=10,\text{ }d=5\]and \[n=25\] \[{{S}_{25}}=\frac{25}{2}\left[ 2(10)+\left( 25-1 \right)5 \right]=1750\] Hence, the total distance the gardener will cover in order to water all the trees \[=2\times 1750=3500\text{ }m\]


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