A species of tree grows in a unique pattern such that its height in a

Question

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.

cdrectenwald · Answer

Can someone explain how they got 97 flowers

EshaFatim · Answer

Flowers are produced only in odd years (n=1,3,5...). For odd year 2n+1, the number of flowers is:
Flowers in year 2n+1 = H2n+1 * n

1. Year 1 (2n+1=1, solving n we get n=0):

Flowers = H1*0 = 3*0 = 0

2. Year 3 (2n+1=3, solving n we get n=1):

Flowers = H3*1 = 11*1 = 11

3. Year 5 (2n+1=5, solving n we get n=2):

Flowers = H5*2 = 43*2 = 86

Total Flowers = 0+11+86 = 97.

Bismuth83 · Answer

1. The question first asks us to find  H_{6} .

2. 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

3. Now the question asks us to find the total number of flower produced from year 1 to 6.

4. 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.

5. Our answer will be:  H_{6}  - 85 and Flowers - 97.

jp11 · Answer

flowers in 1,3,5th year only so n=0,1,2 put values you get no of flowers in  1st year =0  2nd year =11  3rd year =86 so total is 97.

Year	1	2	3	4	5	6
Flowers produced	\(H_{1} * 0\)	0	\(H_{3} * 1\)	0	\(H_{5} * 2\)	0

A species of tree grows in a unique pattern such that its height in a

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\(H_{6}\)	Flowers
		67
		79
		85
		86
		97
		100

GMAT Two-part Analysis (TPA) Questions

A species of tree grows in a unique pattern such that its height in a

Prep Toolkit

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More than Quant/Verbal Abilities: Speed vs. Accuracy

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Perfect 805 Score Debrief by Julia

My Rewards