# Question #76a4c

Feb 28, 2017

${a}_{x} = {3}^{x}$

#### Explanation:

$\textcolor{red}{\text{Corrected logic}}$

Let the count number be $i$
Let the ith value in the sequence by ${a}_{i}$

The sequence for the end of each week:

$\text{start of first week } \to \left[1\right]$

Then we have sequential end of weeks

$\left[1 \times 3 = 3\right] \text{; "[3xx3=9]"; } \left[3 \times 9 = 27\right] \ldots . .$

$i = 1 \to {a}_{1} = 1 \times {3}^{1} = 3$
$i = 1 \to {a}_{2} = 1 \times {3}^{2} = 9$
$i = 3 \to {a}_{3} = 1 \times {3}^{3} = 27$

and so on

So for any $i$ we have ${a}_{i} = {3}^{i}$

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

${a}_{x} = {3}^{x}$

Mar 1, 2017

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

#### Explanation:

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

$\text{ "1," "3," "9," "27," "81," } 243 \ldots$

We should recognise that these are the powers of 3.

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

Weeks: $\text{ "0," "1," "2," "3," "4," } 5 \ldots$

Powers:$\text{ "3^0," "3^1," "3^2," "3^3," "3^4," } {3}^{5} \ldots$
Flowers:$\text{ "1," "3," "9," "27," "81," } 243 \ldots$

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