# What is a quick way to calculate the sequence of the next shape?

#### cvelam

##### New member
What is the 2,784th shape in the sequence? triangle , square, rectangle, circle

#### Dr.Peterson

##### Elite Member
What is the 2,784th shape in the sequence? triangle , square, rectangle, circle

You have not defined a sequence at all, but have merely given four "terms". Therefore, the answer could be anything at all -- or, rather, there is no answer.

#### topsquark

##### Senior Member
What is the 2,784th shape in the sequence? triangle , square, rectangle, circle
How do you get the first steps in this sequence? I'm not coming up with anything.

-Dan

#### cvelam

##### New member
You have not defined a sequence at all, but have merely given four "terms". Therefore, the answer could be anything at all -- or, rather, there is no answer.
The sequence I gave was the terms on the page but they were pictures I could not put in the problem. The picture showed the different shapes in sequence 1st was a triangle 2nd was the square, 3rd was a rectangle and 4th was a circle.

#### topsquark

##### Senior Member
If we look at how many "sides" are in the figures then we have the correspondence:
circle - 0
triangle - 3
square - 4

but the rectangle also has 4 sides so I don't know what to do with that.

The only thing I can guess is that you have a cycle of 4. Thus if you were asked to get the 6th shape in the sequence then you would have
triangle, square, rectangle, circle, triangle, square... so the answer would be square.

But as I said it's only a guess. You need to talk to your instructor.

-Dan

#### Dr.Peterson

##### Elite Member
The sequence I gave was the terms on the page but they were pictures I could not put in the problem. The picture showed the different shapes in sequence 1st was a triangle 2nd was the square, 3rd was a rectangle and 4th was a circle.
The problem, as I stated, is not properly formed, so it really has no answer. You have to guess at what pattern they are assuming, which might depend on something stated or implied in the context. If you showed us an image of the entire page, it might give us some further clues.

One possibility is that the shapes repeat the same four over and over: TSRCTSRC... If so, then every multiple of 4 is a circle, and you can work out an answer from that.

#### JustYourAverageFriend

##### New member
What is the 2,784th shape in the sequence? triangle , square, rectangle, circle
If I interpret this question my way it would be the sequence goes like triangle square rectangle circle triangle square rectangle circle….
That’s four different terms. Divide 2784 by 4 and that gives you 696. That means the sequence goes through 696 times. The last term in your pattern is circle so the 2784th term would be a circle. If there was a remainder 1, it’s a triangle, remainder 2, a square…etc