For The Mathematically Inclined

Problem 1:
A geometric sequence with six members has the sum of all six members equal to 63; the sum of the even members (that has even index) has a value of 42. Find these members.

The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, from the second 4 and keep the third, we get the geometric sequence. What is the largest number of the arithmetic sequence?

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Problems from 1/13/22

Problem 1:
The diagonals in a rhombus ABCD are 6 cm and 8 cm long. What is the perimeter of this rhombus?

Problem 2:

A prism with an altitude of 15cm has a base in the form of a regular octagon inscribed in a square 10cmx10cm. What is the volume of the prism?