An organisation plans to plant saplings in $25$ streets in a town in such a way that one sapling for the first street, two for the second, four for the third, eight for the fourth street and so on. How many saplings are needed to complete the work?

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Solution

The number of saplings to be planted for each of the $25$ streets in the town forms a G.P.
Let $S_{n}$ be the total number of saplings needed.
Then, $S_{n} = 1 + 2 + 4 + 8 + 16 + . . . . to 25 terms$ .
Here, $a = 1, r = 2, n = 25$
$S_{n} = a [\frac{r^{n} - 1}{r - 1}]$
$S_{25} = (1) \frac{[2^{25} - 1]}{2 - 1}$
$= 2^{25} - 1$
Thus, the number of saplings to be needed is $2^{25} - 1$ .

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An organisation plans to plant saplings in 25 streets in a town in such a way that one sapling for the first street, two for the second, four for the third, eight for the fourth street and so on. How many saplings are needed to complete the work?

The number of saplings to be planted for each of the 25 streets in the town forms a G.P. Let Sn be the total number of saplings needed.Then, Sn=1+2+4+8+16+.... to 25 terms.Here, a=1,r=2,n=25Sn=a[rn−1r−1]S25=(1)[225−1]2−1=225−1Thus, the number of saplings to be needed is 225−1.

An organisation plans to plant saplings in $25$ streets in a town in such a way that one sapling for the first street, two for the second, four for the third, eight for the fourth street and so on. How many saplings are needed to complete the work?