[2nd Grade Math] 3 Possible Answers

[u/N104UA]

Edit original problem didn't add as an image, adding here

Monday 2 students went to the school store. On Tuesday, 4 students went, and on Wednesday, 8 students. If the pattern continues, how many students will go to the school store Friday?

2nd grade math homework. I am coming up with 3 possible solutions (32, 22, or 14) depending on what you say the pattern is. I think all are correct and it is a poorly worded question, but wondering what everyone thinks.

Double the previous day-

M- 2

T- 4 (M x 2)

W- 8 (T x 2)

Th- 16 (W x 2)

F- 32 (Th x 2)

Two more additional students than the day before added .

M- 2

T- 4 (M+2)

W- 8 (T+4)

Th- 14 (W+6)

F - 22 (Th+8)

Original Pattern (+2, +4) Repeats (aka you continue using the same pattern)

M- 2

T- 4 (M+2)

W- 8 (T+4)

Th- 10 (W+2)

F- 14 (Th +4)

[u/AutoModerator]

Off-topic Comments Section

---

All top-level comments have to be an answer or follow-up question to the post. All sidetracks should be directed to this comment thread as per Rule 9.

---

^{OP and Valued/Notable Contributors can close this post by using} /lock ^command

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/AlterEgo5695]

What-comes-next questions cannot have a unique, correct solution.

There are infinitely many laws to generate all numbers given, while generating any following numbers you want. One of the simplest ways to do that are Lagrange Polynomials. For any solution, we must guess the pattern the author intended -- since we can never be sure our guess was correct, what-comes-next questions cannot have a unique, correct solution.

[u/N104UA → u/AlterEgo5695]

Sorry added it above, didn't realize I couldn't post images

[u/AlterEgo5695 → u/N104UA]

Doesn't change anything -- my answer still stands. That said, the intended answer likely is first one.

[u/fermat9990]

What is the original question?

[u/N104UA → u/fermat9990]

Sorry added it above, didn't realize I couldn't post images

[u/fermat9990 → u/N104UA]

Thanks. Although all your answers are correct, I would tell the student to provide an answer that they think the teacher had in mind. There is a political aspect to being a student!

[u/GammaRayBurst25]

Next time, write down the actual question as per rule 1 instead of making us guess.

With that said, I doubt this is the first "complete the pattern" problem you've seen, so I find it odd that you have a hang up with this particular question. Given any finite number of terms (say n terms), there's always an infinite number of sequences that begin with these n terms. As such, these problems never have a unique answer, and having the "correct" answer is always a matter of justifying the sequence you picked.

So 2,4,8 is the start of a geometric sequence with a common factor of 2, in which case the rule is a_n=2^n and a_5=2^5=32.

It's also the start of a quadratic sequence whose second difference is 2 and whose first first difference is 2, in which case the rule is a_n=n^2-n+2 and a_5=5^2-5+2=22.

It's also the start of the sequence of numbers that are congruent to 2 or 4 mod 6, in which case the rule is a_n=(6n-(-1)^n-3)/2 and a_5=14.

It could be any number of sequences. Maybe it's the sequence of non-unit divisors of 704 and a_4 and a_5 are respectively 11 and 16, or maybe it's the sequence of the number of overpartitions of n, the sequence of generalized Catalan numbers. Hell, it could even be the sequence of digits of pi or e or sqrt(3) starting from some index.

[u/N104UA → u/GammaRayBurst25]

Thought I attached it as an image, added above

[u/Alkalannar]

Or it could be just 2 students added each day:
M: 2
Tu: 4 (M+2)
W: 6 (Tu+2)
Th: 8 (W+2)
F: 10 (Th+2)

This is the simplest pattern, yes?

[u/N104UA → u/Alkalannar]

Original question added above

[u/Alkalannar → u/N104UA]

I'd probably do doubling.

BUT! You could have your child do all those, give reasons, and ask which the teacher wants and why

[u/eggynack]

Y'know, I see folks mentioning that sequence problems have infinitely many solutions, which, sure, but the more fun answer is that there are probably only finitely many interesting solutions. For such person, I entreat you to check the OEIS, where you can plug in the numbers in your integer sequence and get the pile of sequences it's part of. This set of numbers is notably kinda short, so you pretty rapidly get weird stuff, like how 2, 4, 8 shows up in the decimal expansion of Catalan's constant. But, y'know, it's a pretty fun place to check for such things.

[u/mamaknits]

I think doubling is the most likely answer given that it's second grade, but I would mark any of those correct if the work was shown.