Discover the First 10 Terms of 3 Different Sequences | Easy Sequence Question

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The discussion focuses on identifying the first 10 terms of a sequence defined by the sum of the first n positive integers. The initial terms provided are 1, 3, 6, 10, 15, 21, 28, 36, 45, and 55, which correctly represent the cumulative sums. There is confusion regarding the sequence's definition, as some participants mistakenly list terms that do not align with the specified rule. The correct approach involves adding the integers sequentially, leading to the proper sequence of triangular numbers. Clarification on the sequence's definition is essential for accurate term generation.
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List the first 10 trems of each of these sequences.

i need help with this one:
1.) the sequence whose nth term is the sum of the first n positive integers

1,2,3,6,12,24,48,96...

i'm not really sure if this is correct. what I am doing is just adding the previous numbers together to get an answer.
 
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"the sequence whose nth term is the sum of the first n positive integers"
So for n = 1, add the first 'one' integers: 1
For n = 2, add the first two integers: 1+2 = 3
For n = 3, add the first three integers: 1+2+3 = 6
...
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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