1. sequences

A hardware supplier has designed a series of six plastic containers with lids where each container(after the first) can be placed into the next larger one for storage purposes.The containers are rectangular boxes, and the dimensions of the largest one are 120 cm by 60 cm by 50 cm. The dimensions of each container is decreased by 10 percent with respect to the next larger one.

State the pattern in the sequence

This is what I've done...
The volume of the largest one would be 3600 cm3
The 2 largest would be 3600-360 = 3240 cm3
The 3 one would be 3240 -324 = 2916 cm3

Thanks,
Happy new year!

2. I may not quite understand the question, but I think it means each dimension is decreased by 10%.
So to start:
120x60x50=360000
108x54x45=262440
and so on...

3. Instead of number's lets use x, y and z as the dimensions:

1) xyz
2) (x-10)(y-10)(z-10)
3) (x-20)(y-20)(z-20)
4) (x-30)(y-30)(z-30)
.
.
n) (x-10[n-1])(y-10[n-1])(z-10[n-1])

You can sub in your numbers for x, y and z as given in the question

4. Hello, terminator!

A hardware supplier has designed a series of six plastic containers with lids
where each container can be placed into the next larger one for storage purposes.
The containers are rectangular boxes.
The dimensions of the largest are: $120 \times 60 \times 50$ cm.
The dimensions of each box is decreased by 10% with respect to the next larger one.

State the pattern in the sequence.
The sequence of what? . . . The dimensions? . . . The volume?

I agree with worc3247.
The dimensions are decreased by 10%, not the volume.

The volume of each box is: . $(90\%)^3 \,=\,72.9\%$ of the next larger box.

. . $\begin{array}{cc}\text{Box} & \text{Volume }(cm)^2 \\ \hline
1 & 360,\!000.00000 \\ 2 & 262,\!440.00000 \\ 3 & 191,\!318.76000 \\ 4 & 139,\!471.37600 \\ 5 & 101,\!674.63310 \\ 6 & \;\;74,\!120.80755 \\ \hline \end{array}$