Let x be the current price of the product
1.15 * x = $2..88
So when rearranging the equation, you get:
x = 2.88/1.15 = $2.50 (to the nearest cent)
Answer: ![\bold{a_{n+1}=\dfrac{1}{2}a_n}](https://tex.z-dn.net/?f=%5Cbold%7Ba_%7Bn%2B1%7D%3D%5Cdfrac%7B1%7D%7B2%7Da_n%7D)
<u>Step-by-step explanation:</u>
Term-to-term rule is also called the recursive rule.
The recursive rule for a geometric sequence is:
where
![a_n\ \text{is the previous term}](https://tex.z-dn.net/?f=a_n%5C%20%5Ctext%7Bis%20the%20previous%20term%7D)
- r is the common ratio
The common ratio (r) is the second term divided by the first term <em>(which is the same ratio for each term divided by its previous term) </em>
In the given sequence {64, 32, 16, 8, 4}, ![r=\dfrac{32}{64}\quad \rightarrow \quad r=\dfrac{1}{2}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7B32%7D%7B64%7D%5Cquad%20%5Crightarrow%20%5Cquad%20r%3D%5Cdfrac%7B1%7D%7B2%7D)
So, the recursive rule is: ![{a_{n+1}=a_n\cdot \dfrac{1}{2}](https://tex.z-dn.net/?f=%7Ba_%7Bn%2B1%7D%3Da_n%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D)
9^2 • 9^6 = 9^(2 + 6) = 9^8
Since we have to solve this system graphically, we'll have to draw both lines.
To draw a line, simply build a little tables with two x,y values: for the first line we have
![\begin{array}{c|c}x&-x+3\\0&3\\1&2\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Cc%7Dx%26-x%2B3%5C%5C0%263%5C%5C1%262%5Cend%7Barray%7D)
So, you can draw the points (0,3) and (1,2), connect them, and you'll have the graph of the line ![y=-x+3](https://tex.z-dn.net/?f=y%3D-x%2B3)
For the second line we have
![\begin{array}{c|c}x&x+5\\0&5\\1&6\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Cc%7Dx%26x%2B5%5C%5C0%265%5C%5C1%266%5Cend%7Barray%7D)
So, you can draw the points (0,5) and (1,6), connect them, and you'll have the graph of the line ![y=x+5](https://tex.z-dn.net/?f=y%3Dx%2B5)
Finally, we have to check where the two lines cross. If your drawing is accurate enough, you'll see that the point you're looking for is (-1, 4)
1+1+1+1+1 ...............