In a school, tree planatation on Independence day was arranged. Every student from I standard will plant 2 trees, II standard students will plant 4 trees each, III standard students will plant 8 trees each etc. If there are 5 standard, how many trees are planted by the student of the school ?

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Solution

The correct option is A 62
Number of tree planted by student from I standard $= 2 = 2^{1}$
Number of tree planted by student from II standard $= 4 = 2^{2}$
Number of tree planted by student from III standard $= 8 = 2^{3}$
Number of tree planted by student from IV standard $= 16 = 2^{4}$
Number of tree planted by student from V standard $= 32 = 2^{5}$
Clearly it is an GP with first term $a = 2$ , common ratio $r = 2$ and $n = 5$
Therefore, total trees planted by all students $= S_{5} = \frac{a (r^{5} - 1)}{r - 1} = \frac{2 (2^{5} - 1)}{2 - 1} = 2 \times 31 = 62$

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