Q: What are the first two numbers which are both triangular an square?

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Yes. 1 is both square and triangular.

There are an infinite number of triangular numbers that are also squares. You can generate such numbers using the formula: Sn+1 = 4Sn(8Sn + 1) With the first Sn being 1. This gives the next such number as: Sn+1= 4 (8 + 1) = 36 You can then plug that into the equation to get: Sn+1 = 4 x 36 (8 x 36 + 1) = 41616 and so on.

1225

7 of the first 15 triangular numbers (462/3 percent) are even.1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120 ...From this fragment of the series, it sure begins to look as if every second pairof triangular numbers are both even, and that 50% of all of them are.

There are many possible answers but the most likely one, for your level, is a triangular prism.

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if you don't count 0 or 1, I believe it's 36 and 1225.

Yes. 1 is both square and triangular.

There are an infinite number of triangular numbers that are also squares. You can generate such numbers using the formula: Sn+1 = 4Sn(8Sn + 1) With the first Sn being 1. This gives the next such number as: Sn+1= 4 (8 + 1) = 36 You can then plug that into the equation to get: Sn+1 = 4 x 36 (8 x 36 + 1) = 41616 and so on.

they are both types of pyramidsThey're both triangular pyramids, and all of them have a base, multiple faces, and at one end the faces come to a point.* * * * *They are NOT both triangular pyramids!

Yes

1 and 36

1225

7 of the first 15 triangular numbers (462/3 percent) are even.1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120 ...From this fragment of the series, it sure begins to look as if every second pairof triangular numbers are both even, and that 50% of all of them are.

There are many possible answers but the most likely one, for your level, is a triangular prism.

both have lateral face shapes that are riangles

Both have 4 vertices, though he vertices of a square are 2 dimensional vertices while those of a triangular pyramid are 3-d.

28 and 10 are both triangular numbers and add up to 38