Question

A geometric progression is a sequence of numbers in which each value (after the first) is obtained by multiplying the previous value in the sequence by a fixed value called the common ratio. for example the sequence 3, 12, 48, 192, ... is a geometric progression in which the common ratio is 4. given the positive integer ratio greater than 1, and the non-negative integer n, create a list consisting of the geometric progression of numbers between (and including) 1 and n with a common ratio of ratio. for example, if ratio is 2 and n is 8, the list would be [1, 2, 4, 8]. associate the list with the variable geom_prog.

Answer 1

To create a geometric progression list between 1 and n with a common ratio, start with 1 and multiply it by the common ratio until you reach n.

Step-by-step explanation:

A geometric progression is a sequence of numbers in which each value (after the first) is obtained by multiplying the previous value in the sequence by a fixed value called the common ratio.

To create a list consisting of the geometric progression of numbers between (and including) 1 and n with a common ratio of ratio, you can start with 1 and keep multiplying it by the common ratio until you reach n or a value greater than n. For example, if the common ratio is 2 and n is 8, the list would be [1, 2, 4, 8].

Here's an example:

• Common ratio (ratio): 2
• Number (n): 8
• Geometric progression list (geom_prog): [1, 2, 4, 8]

Answer 2

The geometric progression with common ratio as 'r', first term as 'a' and nth term as 'n' is a,ar,ar^{2}, ar^{3},.....ar^{n-1}.

Let the common ratio(r) be 3 and n be 27.

Let the first term(a) of the sequence = 1

Second term of the sequence= ar= 1 x 3= 3

Third term of the sequence= ar^{2}= 1 x 3^{2}= 9

Fourth term of the sequence= ar^{3}= 1 x 3^{3}= 27

So, the list of numbers with r=3 and n=27 is [1,3,9,27].