Question

Amber is starting a garden. She plants 2 flowers the first month. The next month, she plans three times more flowers (6 flowers). Each month, Amber plants three times more flowers than the previous month. How many flowers will Amber plant in the 4th month? A. Write a number sentence. (2 × 4) + 2 + 6 = x Multiply 2 flowers by the 4th month, then add the number of flowers from the first and second month. B. Make a table. In the first row, write 1st month - 2 flowers. In the next row, write 2nd month - 3 flowers. In the third row, write 3rd month - 4 flowers. Continue the pattern to find how many flowers Amber will plant in the fourth month. C. Draw a diagram. Use dots to represent flowers. Draw 2 dots for the first month. Draw 6 dots for the next month. Do this two more times and keep tripling the previous number of flowers to find the number of flowers planted in the fourth month.

Answer 1

This is a geometric progression problem. We can the general formula that can tell us how many flowers would be planted each month.
Let's write the terms that we know and see if we can find the pattern:
$\begin{tabular}{lll} Month & Number of flowers planted & Different form \\ 1 & 2 & 2\cdot3^0 \\ 2 & 6 & 2\cdot3^1 \\ 3 & 18 & 2\cdot3^2 \\ 4 & 54 & 2\cdot3^3 \end{tabular} \end{table}$
The patern here is obvious. Let's write it down:
$N=2\cdot3^{n-1}$
This formula gives us a number of flowers planted in the n-th month.