Question

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

Answer 1

Answer:

423644304721 saplings

Step-by-step explanation:

The organization plans to plant the saplings in 25 streets.

1 sapling for the first street,

3 for the second,

9 for the third,

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25 streets.

So, we can understand that the organization is using a geometric series.

Let a = 1,

     r = 3,

    n = 25

The series is;

a + $ar^{2}$ + $ar^{3}$ + ......... $ar^{n-1}$

The first street = a = 1 sapling

The second street = $ar^{2}$ =  $1*3^{2}$ = 3

The third street =  $ar^{3}$ =  $1*3^{3}$ = 9

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The 25th street =  $ar^{24}$ =  $1*3^{24}$

If a series is as follows;

a + $ar^{2}$ + $ar^{3}$ + ......... $ar^{n-1}$

Sum (S) = ($3^{n}$ - 1)/2

             = ($3^{25}$ -1)/2

             = (847288609443 - 1)/2

             = 847288609442/2

             = 423644304721

Therefore, the number of saplings needed to complete the work = 423644304721

Answer 2

Answer:

2^25 -1

Step-by-step explanation:

sn= 1+2+4+8+....to 25 terms

a=1, r= 2 n=25

sn = a[2^25-1]/2-1

sn=2^25 -1