codysaucier2823
16.10.2020 •
Mathematics
i need help with this questions asap please. A grocery clerk is making a display of oranges. The numbers of oranges in the layers of the display form a sequence, with the top layer counting as layer 1. The explicit rule f(n) = (n + 1)2 describes this sequence, where n is a whole number greater than 0. Will 50 oranges be enough to complete the top 4 layers of the display?
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Ответ:
If there is 1 at the top, then you have 1, then 2, then 3, etc.
total number of oranges equals:
1 + 2 + 3 + ... + 16 + 17 + 18 <-- stop at 18 because this is the number of oranges at the base
You can use the formula:
sum of first n numbers = n*(n + 1)/2
-->
18*19/2 = 9*19 = 171
or you can figure it out (basically derive the above formula):
you have:
1 + 18 = 19
2 + 17 = 19
3 + 16 = 19
...
How many pairs do you have? Well, it's just the number of numbers: 1-18 = 18 numbers (divide by 2) = 9 pairs)
9 pairs of 19 = 9 * 19 = 171
Hope this helps!
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