The total number of lotuses in a lake grows in such a way that their number increases twice the previous day. For e.g. If there are $ x $ lotuses on 1st day, then on 2nd day there will be $ 2 x $ lotuses, 3rd day there will be $ (2 \times 2 x=4 x) $ lotuses and so on. If there are 255 lotuses on 5th day, find the total number of lotuses on 7th day.

Given:

The total number of lotuses in a lake grows in such a way that their number increases twice the previous day.

There are 255 lotuses on 5th day To do:

We have to find the total number of lotuses on 7th day.

Solution: According to the given question,

If there are $x$ lotuses on 1st day, the number of lotuses on nth day$=2^{n-1}x$.

Let the number of lotuses on 1st day be $x$.

The number of lotuses on 5th day$=2^{5-1}x$

$2^4x=255$

$x=\frac{255}{16}$

The number of lotuses on 7th day$=2^{7-1}x$

$=2^6\times\frac{255}{16}$

$=64\times\frac{255}{16}$

$=4\times255$

$=1020$

There are 1020 lotuses on 7th day.

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