Answer:
see below
Step-by-step explanation:
1. a = 18, 2. n = -19, 3. x = -17, 4. v = -6, 5. a = 9, 6. x = -2, 7. k = -4, 8. m = -19
9. n = 3, 10. a = -7, 11. n = -5, 12. n = -6, 13. x = -1/3, 14. m = 2/3 15. m = -9.8
16. n = 7.9, 17. x = 0, 18. b = 2, 19. v = -8, 20. b = -4, 21. n = 3, 22. p = 3.3
Answer:
48 1/4 packages
Step-by-step explanation:
Answerthats good
Step-by-step explanation:
i will answer
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
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