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.

Question

Mathematics

Jayleen

2 July, 09:20

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.

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Beckett Gibson · Answer 1

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].