Asked by Brenda

Algebra 2
A sequence is of pyramids is created where the first pyramid has a height of 6 inches and a base area of 10 inches, for a volume of 20 cubic inches. The height of the next pyramid is twice the height of the previous pyramid. The input of the sequence is the position of the pyramid and the output is the volume of the pyramid. Is the sequence explicit or recursive? Is the sequence arithmetic, geometric, or neither?
I don't understand and don't know where to start from to find the answer out please help
Answered by Reiny
Confusing wording:
"he first pyramid has a height of 6 inches and a base area of 10 inches"
since you tell us the volume is 20 inches^2 , the base are must be 10 inches^2

I also will assume that the base does not change

volume of 1st pyramid = (1/3)(10)(6) = 20
volume of 2nd pyramid = (13)(10)(12) = 40
volume of 3rd ---- = (1/3)(10)(24) = 80

20, 40, 80, ... clearly show a geometric sequence

I could write the volume either as an explicit expression or a recursive

explicit: ----> V(n) = 10(2)^n
recursive ---> V(n) = 2V(n-1), n > 1, V(1) = 20
Answered by Brenda
but where do i get the 1/3 from?
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