# Find the Next Term in the Math Sequence?

• johnqwertyful
In summary: You are right, of course. In the context of the assignment, the "obvious" answer is 25 because it follows the pattern of n^2 and the previous terms in the sequence. But as you pointed out, there are many other possible answers that could follow a different pattern. This highlights the importance of considering all possibilities and not just relying on intuition or incomplete information. It also brings up the question of whether this type of assignment is truly beneficial in teaching students math. In summary, the debate over whether to continue giving assignments that require students to find the next term in a sequence is ongoing. On one hand, it teaches pattern recognition and intuition, but on the other hand, it may lead to drawing conclusions from incomplete information. It
johnqwertyful
"Find the next term"

After studying more math, I've been conflicted about this type of assignment commonly given to high schoolers. In the sequence 1, 4, 9, 16, ____ find the next term.

On one hand, it's a good exercise and teaches pattern recognition. On the other though, it seems to go against a lot of math. 25 is the "obvious" choice, but is 25 any more correct than say, -43? Just because n^2 is A rule, and probably the "simplest" doesn't make it any more correct than any other rule. It seems to teach students to draw conclusions from incomplete information.

It DOES seem useful to teach kids pattern recognition and intuition. But is it really worth it? Or would there be a better way?

It teaches students intuition
It has its own worth

Remember it is very important in real life to draw conclusions from incomplete information

Remember the difference between deduction and induction. Both are very important in mathematical reasoning

johnqwertyful said:
After studying more math, I've been conflicted about this type of assignment commonly given to high schoolers. In the sequence 1, 4, 9, 16, ____ find the next term.

On one hand, it's a good exercise and teaches pattern recognition. On the other though, it seems to go against a lot of math. 25 is the "obvious" choice, but is 25 any more correct than say, -43? Just because n^2 is A rule, and probably the "simplest" doesn't make it any more correct than any other rule. It seems to teach students to draw conclusions from incomplete information.

It DOES seem useful to teach kids pattern recognition and intuition. But is it really worth it? Or would there be a better way?

Actually, I rather agree with you.
Getting 25 rests on an UNSTATED premise of Occam's Razor application, i.e, we are to find the arguably simplest pattern those 4 instances would be the first four examples of.

Furthermore, to discipline the mind to "think simple" when doing maths is, actually, precisely the challenge those not doing well in maths have difficulties in.

And if the next term in the sequence were -43, how to explain the sequence?

SteamKing said:
And if the next term in the sequence were -43, how to explain the sequence?
I've no idea what was in johnqwertyful's mind but one possible answer is$$\frac{(n-2)(n-3)(n-4)(n-5)}{(1-2)(1-3)(1-4)(1-5)} + 4\frac{(n-1)(n-3)(n-4)(n-5)}{(2-1)(2-3)(2-4)(2-5)} + 9\frac{(n-1)(n-2)(n-4)(n-5)}{(3-1)(3-2)(3-4)(3-5)} \\ + 16\frac{(n-1)(n-2)(n-3)(n-5)}{(4-1)(4-2)(4-3)(4-5)} - 43\frac{(n-1)(n-2)(n-3)(n-4)}{(5-1)(5-2)(5-3)(5-4)}$$ Clearly an absurdly complicated answer but nevertheless valid. (And you could use this method to get any answer for any sequence.)

SteamKing said:
And if the next term in the sequence were -43, how to explain the sequence?

A sequence is just a function ##\mathbb{N}\rightarrow \mathbb{R}##. Nobody said we can 'explain' (= give a general term for) any sequence. In fact, we can't for most sequences.

The rule of thumb is to keep it simple. There is no need to complicate things at all if it's not really necessary. Something I noticed while in uni, those in engineering insist on the simplest Working solution - the evolution of technology really does lie in simplicity, but it's so elusive, which makes it ingenious and that's why people go haywire.."zommmg he's a genius!". Those in theoretical sciences, en masse, have some kind of inexplicable urge to blow everything out of proportion. :/ One of my friends in psychology carried out a small research between the students of 4 universities and pretty much confirmed my hunch. Of, course it isn't the whole information, but how much are you going to push the envelope? Eventually, what even is complete information? Perfectionists aren't welcome in my house, no offense. I'll get you some coffee or tea, but no cake, since that would become too much of a science.

DrGreg said:
I've no idea what was in johnqwertyful's mind but one possible answer is$$\frac{(n-2)(n-3)(n-4)(n-5)}{(1-2)(1-3)(1-4)(1-5)} + 4\frac{(n-1)(n-3)(n-4)(n-5)}{(2-1)(2-3)(2-4)(2-5)} + 9\frac{(n-1)(n-2)(n-4)(n-5)}{(3-1)(3-2)(3-4)(3-5)} \\ + 16\frac{(n-1)(n-2)(n-3)(n-5)}{(4-1)(4-2)(4-3)(4-5)} - 43\frac{(n-1)(n-2)(n-3)(n-4)}{(5-1)(5-2)(5-3)(5-4)}$$ Clearly an absurdly complicated answer but nevertheless valid. (And you could use this method to get any answer for any sequence.)

Where did the problem state "you MUST use Occam's razor here!"?

lendav_rott said:
The rule of thumb is to keep it simple.
An where, in these problem texts is the rule to apply Occam's Razor stated??

DrGreg said:
I've no idea what was in johnqwertyful's mind but one possible answer is$$\frac{(n-2)(n-3)(n-4)(n-5)}{(1-2)(1-3)(1-4)(1-5)} + 4\frac{(n-1)(n-3)(n-4)(n-5)}{(2-1)(2-3)(2-4)(2-5)} + 9\frac{(n-1)(n-2)(n-4)(n-5)}{(3-1)(3-2)(3-4)(3-5)} \\ + 16\frac{(n-1)(n-2)(n-3)(n-5)}{(4-1)(4-2)(4-3)(4-5)} - 43\frac{(n-1)(n-2)(n-3)(n-4)}{(5-1)(5-2)(5-3)(5-4)}$$ Clearly an absurdly complicated answer but nevertheless valid. (And you could use this method to get any answer for any sequence.)

Even better than that:
S1=1, S2=4, S3=9, S4=16, S5=-43

This is a perfectly valid sequence. You don't need to come up with a cute formula, you just need to ASK for what you want.

## What is a math sequence?

A math sequence is a list of numbers that follow a specific pattern or rule. The numbers in the sequence are called terms.

## How do I find the next term in a math sequence?

To find the next term in a math sequence, you must identify the pattern or rule that the sequence follows. Then, you can apply that pattern or rule to the previous terms to determine the next term.

## What are some common patterns in math sequences?

Some common patterns in math sequences include arithmetic sequences, where each term is found by adding a constant value to the previous term, and geometric sequences, where each term is found by multiplying a constant value to the previous term.

## Why is it important to find the next term in a math sequence?

Finding the next term in a math sequence can help you predict future values in the sequence and make informed decisions based on the pattern or rule that the sequence follows. It is also an important skill in solving more complex math problems.

## Are there any strategies for finding the next term in a math sequence?

Yes, there are several strategies you can use to find the next term in a math sequence. Some common strategies include identifying the type of sequence (arithmetic, geometric, etc.), looking for patterns in the differences between terms, and using algebraic equations to represent the sequence.

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