Question

Question #76a4c

Answer 1

`a_x=3^(x)`

Explanation:

`color(red)("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:

`"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

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:

`" "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`