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13 Mar 2025, 04:29
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\(H_{6}\): 85
Flowers: 97
A species of tree grows in a unique pattern such that its height in a given year follows a sequence defined as:
• \(H_{n} = H_{n-1} + 2 * H_{n-2}\)
where \(H_{1} = 3\) meters and \(H_{2} = 5\) meters, and \(H_{n}\) is the height of the tree in meters at the end of year \(n\).
The tree produces flowers in odd years (e.g., 1, 3, 5, 7, ...). The number of flowers produced in year \(2n+1\) is equal to the value of \(H_{2n+1} * n\).
Based on the above information, select for \(H_{6}\) the height of the tree in year 6 and for Flowers the total amount of flowers produced from year 1 to 6.
• \(H_{n} = H_{n-1} + 2 * H_{n-2}\)
where \(H_{1} = 3\) meters and \(H_{2} = 5\) meters, and \(H_{n}\) is the height of the tree in meters at the end of year \(n\).
The tree produces flowers in odd years (e.g., 1, 3, 5, 7, ...). The number of flowers produced in year \(2n+1\) is equal to the value of \(H_{2n+1} * n\).
Based on the above information, select for \(H_{6}\) the height of the tree in year 6 and for Flowers the total amount of flowers produced from year 1 to 6.
| \(H_{6}\) | Flowers | |
| 67 | ||
| 79 | ||
| 85 | ||
| 86 | ||
| 97 | ||
| 100 |
ShowHide Answer
Official Answer
\(H_{6}\): 85
Flowers: 97
13 Mar 2025, 04:29
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Official Solution:
The question first asks us to find \(H_{6}\).
Let’s list do the calculations for the first few terms:
- \(H_{3} = H_{2} + 2 * H_{1} = 5 + 2 * 3 = 11\)
- \(H_{4} = H_{3} + 2 * H_{2} = 11 + 2 * 5 = 21\)
- \(H_{5} = H_{4} + 2 * H_{3} = 21 + 2 * 11 = 43\)
- \(H_{6} = H_{5} + 2 * H_{4} = 43 + 2 * 21 = 85\)
Now the question asks us to find the total number of flower produced from year 1 to 6.
Let’s write out a table with the number of flowers made each year.
Or:
That means the total number of flowers will be 86 + 11 = 97.
Our answer will be: \(H_{6} - 85\) and Flowers - 97.
Correct answer:
\(H_{6}\) "85"
Flowers "97"
Bunuel
The question first asks us to find \(H_{6}\).
Let’s list do the calculations for the first few terms:
- \(H_{3} = H_{2} + 2 * H_{1} = 5 + 2 * 3 = 11\)
- \(H_{4} = H_{3} + 2 * H_{2} = 11 + 2 * 5 = 21\)
- \(H_{5} = H_{4} + 2 * H_{3} = 21 + 2 * 11 = 43\)
- \(H_{6} = H_{5} + 2 * H_{4} = 43 + 2 * 21 = 85\)
Now the question asks us to find the total number of flower produced from year 1 to 6.
Let’s write out a table with the number of flowers made each year.
| Year | 1 | 2 | 3 | 4 | 5 | 6 |
| Flowers produced | \(H_{1} * 0\) | 0 | \(H_{3} * 1\) | 0 | \(H_{5} * 2\) | 0 |
Or:
| Year | 1 | 2 | 3 | 4 | 5 | 6 |
| Flowers produced | 0 | 0 | 11 | 0 | 86 | 0 |
That means the total number of flowers will be 86 + 11 = 97.
Our answer will be: \(H_{6} - 85\) and Flowers - 97.
Correct answer:
\(H_{6}\) "85"
Flowers "97"
08 Apr 2025, 07:29
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This question took me 7 minutes to solve. Please help figure out a faster way to solve it and links to similar questions for practice would be much appreciated
