Q: Which explains why the sequence 216 12 23 is arithmetic or geometric?

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729

64 125 216 343 512 729Bold numbers are the missing in the sequence

343.

In simpler terms, a geometric sequence is a sequence in which some constant (same) number multiplies every-time to give u the next number in the sequence. 2, 4, 6, 8, 10, 12 - The constant is 2 (E.g. 2 x 2 = 4) 6, 36, 216, 1296, 7776 - The constant is 6 (E.g. 6 x 6 = 36) ------------------------------------------------------------------------------------------------------------------ To figure out the constant number we just divide one number in the sequence by the one next to it on the left. E.g. 36/6 = 6 ++++ That first example, starting at 2 with a constant=2, is arithmetical not geometrical because it simply adds 2 each time. If the constant is a multiplier the series is 2, 4, 8, 16, 32, 64, ...

tn = n3

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No it is not.

216

64

216. That is because 125 is 5 cubed and 343 is 7 cubed, so 6 cubed is 216.

729

64 125 216 343 512 729Bold numbers are the missing in the sequence

343.

In simpler terms, a geometric sequence is a sequence in which some constant (same) number multiplies every-time to give u the next number in the sequence. 2, 4, 6, 8, 10, 12 - The constant is 2 (E.g. 2 x 2 = 4) 6, 36, 216, 1296, 7776 - The constant is 6 (E.g. 6 x 6 = 36) ------------------------------------------------------------------------------------------------------------------ To figure out the constant number we just divide one number in the sequence by the one next to it on the left. E.g. 36/6 = 6 ++++ That first example, starting at 2 with a constant=2, is arithmetical not geometrical because it simply adds 2 each time. If the constant is a multiplier the series is 2, 4, 8, 16, 32, 64, ...

Each number is 60 percent of the previous one.

tn = n3

216, 432, 864.... Just keep multiplying the number by 2.

The sequence is the cube of successive numbers starting at 1; 13 - 23 - 33 - 43 - 53 - 63 -...