Zeke has swim club every 2 days and robotics club every 8 days. This month, he has swim club on the 2nd day of the month and robotics club on the 8th day of the month.
Zeke says that the first time he will have both clubs on the same day is the 16th day of the month because the LCM of 2 and 8 is 16.

Does Zeke’s reasoning make sense? Use the drop-down menus to explain.

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Zeke found the LCM to be the product of
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,

but because 8 is a
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of 2, the LCM is
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.

So the first day he will have both clubs is the
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day of the month.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

80x^8−68x^6+16^5−20x^4−4x^3+8x^2

hope i'm right lol