In a school, tree plantation 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 that school ?

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Solution

The numbers of trees in the school are in G.P., i.e., 2, 4, 8,…
In the given G.P., we have:
t₁ = 2, t₂ = 4 and t₃ = 8
Thus, we have the first term as a = t₁ = 2 and the common ratio as $r = \frac{t_{2}}{t_{1}} = \frac{4}{2} = 2 > 1$ .
We know:
Sum of the first n^thterm of the G.P., $S_{n} = \frac{a (r^{n} - 1)}{r - 1} for r > 1$
To find S₅, we will put a = 2, r = 2 and n = 5 in the above equation.
Thus, we get:

$S_{5} = \frac{2 (2^{5} - 1)}{2 - 1} = \frac{2 (32 - 1)}{1} = 2 \times 31 = 62$

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