Question

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 ?

Answer 1

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^th term of the G.P., $S_n=\frac{a\left(r^n-1\right)}{r-1}\mathrm{for}r>1$
To find S₅, we will put a = 2, r = 2 and n = 5 in the above equation.
Thus, we get:

$$\begin{gathered} S_5=\frac{2\left(2^5-1\right)}{2-1} \\ =\frac{2\left(32-1\right)}{1} \\ =2\times 31=62 \end{gathered}$$