Respuesta :
There is need of total of 9 levels to stack 285 boxes.
What is a sequence ?
A sequence can be taken as the set of numbers having a particular order for all the terms or we can say that arrangement of numbers in some order is known as sequence.
Some examples for sequence are :
2,4,6,8,10,12
3,9,27,81,243
What is recursive sequence ?
The recursive sequence is the sequence in which any term in the sequence can be find with the help of previous term of that sequence.
In a sequence , first term always known as initial term.
and difference between two terms are known as common difference. It is denoted by d.
General form of sequence is :
[tex]a_1,a_2,a_3,----,a_n[/tex]
where , [tex]a_n[/tex] = last term in sequence.
According to question,
Also, number of boxes at level recursively n =[tex]a_{n-1} + n^2[/tex]
The formula to find number of level for 285 boxes is :
[tex]a_n > =285[/tex]
now, find each level
[tex]a_1 = 1 , a_2 = 1 + 2^2 = 5 , a_3 = 5+3^2 = 14,\\a_4 = 14 + 4^2 = 30\\a_5 = 30 + 5^2 = 55\\a_6 = 55 + 6^2 = 91\\a_7 = 91 + 7^2 = 140\\a_8 = 140 + 8^2 = 204\\a_9 = 204 +9^2 = 285[/tex]
thus, to stack 285 boxes total numbers of level are 9.
To know more about recursive sequence, visit :
https://brainly.com/question/8972906
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The complete question is :
Suppose you're stacking boxes in levels which make squares. The numbers of boxes in each successive levels make a sequence. The figure show top four levels as view from top or above.
a. How many boxes of same size would need for next lower level?
b. How many boxes of same size would need to add the 3 levels?
c. Suppose you are stacking 285 boxes. Then, how many total levels will you have?
