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Answer 1 · 2017-02-28T15:25:57

$a_{x} = 3^{x}$ $a_x=3^(x)$

$Corrected logic$ $color(red)("Corrected logic")$

Let the count number be $i$ $i$
Let the ith value in the sequence by $a_{i}$ $a_i$

The sequence for the end of each week:

$start of first week \to [1]$ $"start of first week "-> [1]$

Then we have sequential end of weeks

$[1xx3=3]"; "[3xx3=9]"; "[3xx9=27].....$

$i=1->a_1=1xx3^1=3$
$i=1->a_2=1xx3^2=9$
$i=3->a_3=1xx3^3=27$

and so on

So for any $i$ we have $a_i=3^(i)$

The question uses $x$ for any term count so we have

$a_x=3^(x)$

Answer 2 · 2017-03-01T12:37:17

The number of flowers after $x$ weeks is given by: $3^x$

We can show the numbers of flowers as a sequence first, with each term being multiplied by 3 to get to the next:

$" "1," "3," "9," "27," "81," "243 ...$

We should recognise that these are the powers of 3.

Compare this with the number of weeks and powers of 3:

Weeks: $" "0," "1," "2," "3," "4," "5 ...$

Powers: $" "3^0," "3^1," "3^2," "3^3," "3^4," "3^5 ...$
Flowers: $" "1," "3," "9," "27," "81," "243 ...$

Therefore, after $x$ weeks, the number of flowers will be $3^x$