How many sides does a pentagon have?

No , the y-values of a data set cannot have both a common difference and a common ratio at the same time.

What is Arithmetic and geometric progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

Thus nth term of an AP series is Tn = a + (n - 1) d

d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

Given data ,

A common difference means that the difference between any two consecutive y-values in the data set is the same. For example, if the first y-value is 3 and the common difference is 2, then the second y-value would be 5 (3 + 2), the third y-value would be 7 (5 + 2), and so on. This creates a linear relationship between the y-values.

And , a common ratio means that the ratio between any two consecutive y-values in the data set is the same. For example, if the first y-value is 3 and the common ratio is 2, then the second y-value would be 6 (3 x 2), the third y-value would be 12 (6 x 2), and so on. This creates an exponential relationship between the y-values.

Hence , a linear relationship and an exponential relationship are different, it is not possible for the y-values of a data set to have both a common difference and a common ratio at the same time.

To learn more about arithmetic and geometric progression click :

brainly.com/question/1522572

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