The recursive formula for given sequence is: ![a_n = a_{n-1}-7](https://tex.z-dn.net/?f=a_n%20%3D%20a_%7Bn-1%7D-7)
And the terms will be expressed as:
![a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\](https://tex.z-dn.net/?f=a_1%20%3D%2011%5C%5Ca_2%20%3D%20a_%7B2-1%7D%20-%207%20%5C%5Ca_2%3D%20a_1%20-%207%5C%5Ca_2%20%3D%2011-%207%5C%5Ca_2%20%3D%204%5C%5Ca_3%20%3D%20a_%7B3-1%7D%20-%207%20%5C%5Ca_3%3D%20a_2%20-%207%5C%5Ca_3%20%3D%204%20-%207%5C%5Ca_3%20%3D%20-3%5C%5Ca_4%20%3D%20a_%7B4-1%7D%20-%207%20%5C%5Ca_4%3D%20a_3%20-%207%5C%5C%20a_4%3D%20-3%20-%207%5C%5Ca_4%20%3D%20-10%5C%5Ca_5%20%3D%20a_%7B5-1%7D%20-%207%20%5C%5Ca_5%3D%20a_4%20-%207%5C%5Ca_5%20%3D%20-10%20-%207%5C%5Ca_5%20%3D%20-17%5C%5C)
Step-by-step explanation:
First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio
Given sequence is:
11,4,-3,-10,-17...
Here
![a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7](https://tex.z-dn.net/?f=a_1%20%3D%2011%5C%5Ca_2%20%3D%204%5C%5Ca_3%20%3D%20-3%5C%5CSo%2C%5C%5Cd%20%3D%20a_2%20-%20a_1%20%3D%204-11%20%3D%20-7%5C%5Cd%20%3D%20a_3-a_2%20%3D%20-3-4%20%3D%20-7)
As the common difference is same, given sequence is an arithmetic sequence.
A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference
So, the recursive formula for an arithmetic sequence is given by:
![a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7](https://tex.z-dn.net/?f=a_n%20%3D%20a_%7Bn-1%7D%20%2Bd%5C%5CPutting%5C%20d%20%3D%20-7%5C%5Ca_n%20%3D%20a_%7Bn-1%7D-7)
Hence,
The recursive formula for given sequence is: ![a_n = a_{n-1}-7](https://tex.z-dn.net/?f=a_n%20%3D%20a_%7Bn-1%7D-7)
And the terms will be expressed as:
![a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\](https://tex.z-dn.net/?f=a_1%20%3D%2011%5C%5Ca_2%20%3D%20a_%7B2-1%7D%20-%207%20%5C%5Ca_2%3D%20a_1%20-%207%5C%5Ca_2%20%3D%2011-%207%5C%5Ca_2%20%3D%204%5C%5Ca_3%20%3D%20a_%7B3-1%7D%20-%207%20%5C%5Ca_3%3D%20a_2%20-%207%5C%5Ca_3%20%3D%204%20-%207%5C%5Ca_3%20%3D%20-3%5C%5Ca_4%20%3D%20a_%7B4-1%7D%20-%207%20%5C%5Ca_4%3D%20a_3%20-%207%5C%5C%20a_4%3D%20-3%20-%207%5C%5Ca_4%20%3D%20-10%5C%5Ca_5%20%3D%20a_%7B5-1%7D%20-%207%20%5C%5Ca_5%3D%20a_4%20-%207%5C%5Ca_5%20%3D%20-10%20-%207%5C%5Ca_5%20%3D%20-17%5C%5C)
Keywords: arithmetic sequence, common difference
Learn more about arithmetic sequence at:
#LearnwithBrainly
Answer:
-1425
Step-by-step explanation:
Day 1 - 475
Day 2 -475
Day 3 - 475
-475+ -475 + -475 = -1425
Answer:
43°
Step-by-step explanation:
The angle of a straight line is 180°, 62° and 75° of the angle is taken so what is remaining is the angle for BEC.
180-(62+75)
180-137
43°
Okay :)
Well first you need to do the multiplication.
5*2/5n=40*5
So 5*2=10 and 40 * 5=200
So now plug those numbers into the equation.
10/5n=200
Now we divide :) So 10/5=2
So what do we have left over??
2n=200
To find n we are just going to divide both sides by 2 so
200/2=100
So n=100
Hope this helps! If you need anymore help or further explanation jsut let me know!!! :)
If the can's combined lips measure 38 inches and the adhesive overlaps by around 12 inches, the label's surface area will be 50 square inches.
<h3>What is the area?</h3>
The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
Given data;
Height of can,![\rm H=5 \frac{3}{8} \ inch](https://tex.z-dn.net/?f=%5Crm%20H%3D5%20%5Cfrac%7B3%7D%7B8%7D%20%20%5C%20inch)
Height of label,
![\rm h=5\frac{3}{8} -\frac{3}{8} \\\\ h= 5 \ inch](https://tex.z-dn.net/?f=%5Crm%20h%3D5%5Cfrac%7B3%7D%7B8%7D%20-%5Cfrac%7B3%7D%7B8%7D%20%5C%5C%5C%5C%20h%3D%205%20%5C%20inch)
Diameter,![\rm d= 3 \ inch](https://tex.z-dn.net/?f=%5Crm%20d%3D%203%20%5C%20inch)
The area of the label is;
A = ( overlap area + circumfereence ) h
![\rm A = [\frac{1}{2} + 2 \pi \times \frac{3}{2} ] \\\\ A =[ \frac{1+6\pi}{2} ] \times 5 \\\\ A = 49.6 \ inch^2](https://tex.z-dn.net/?f=%5Crm%20A%20%3D%20%5B%5Cfrac%7B1%7D%7B2%7D%20%2B%202%20%5Cpi%20%5Ctimes%20%5Cfrac%7B3%7D%7B2%7D%20%5D%20%5C%5C%5C%5C%20A%20%3D%5B%20%5Cfrac%7B1%2B6%5Cpi%7D%7B2%7D%20%5D%20%5Ctimes%205%20%5C%5C%5C%5C%20A%20%3D%2049.6%20%5C%20inch%5E2)
Hence, the label's surface area will be 50 square inches.
To learn more about the area, refer to the link;
brainly.com/question/11952845
#SPJ1