Sequences: Plugging In

The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year minus the age of the tree in years (rounded down to the nearest integer). During its third year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its sixth year?

Incorrect. [[snippet]] You overshot the mark a bit there.… Were you looking for the value of $$A_6$$ perhaps?

Incorrect. [[snippet]] The number 35 is the answer you get when you assume that the tree is three years old (instead of two years old) during its third year.

If you are confused why the third year gives $$A_2 = 50$$, think about a newborn baby: The baby is in its first year, but the age of the baby is not 1 yet. It is not until the baby starts its second year (on its birthday) that we say it is one year old. Similarly, during the baby's third year, the baby is two years old (or two and one-half years old, etc., but the question says to round down). So the question tells you that $$A_2= 50$$ because the age during the third year rounds down to 2.

Incorrect. [[snippet]]

Incorrect. [[snippet]] The number 43 is one of the terms in this sequence, but it is not the right one. Keep going!

Correct. [[snippet]] Use the rule to calculate the number of plums during the fourth, fifth, and sixth years: >Fourth Year: $$A_3 = A_2 - 3 = 50 - 3 = 47$$ >Fifth Year: $$A_4 = A_3 - 4 = 47 - 4 = 43$$ >Sixth Year: $$A_5 = A_4 - 5 = 43 - 5 = 38$$

43

41

38

35

32

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