determine if the sequence is arithmetic or geometric and determine the common difference / ratio in simplest form 15,10,5

The sequence is arithmetic progression and the common difference is -5

Step-by-step explanation:

AP = a + (n -1)d

a = first number = 15

d = common difference

Using the second term

10 = 15 + (2-1) d

10 = 15 + (1)d

10 = 15 + d

10-15 = d

d = -5

Using the third term

5 = 15 + (3-1) d

5 = 15 + (2)d

5 = 15 + 2d

5-15 = 2d

-10 = 2d

-10/2 = d

-5 = d

For the Geometric Progression,

GP = ar^n-1

a = first number

r = common ratio

Using the second number of the series

10 = 15 × r^2-1

10/15 = r^1

-2/3 = r

Using the second number of the series

5 = 15 × r^3-1

5/15 = r^2

-1/3 = r^2

r = square root of -1/3

Conclusion: From the above calculations, the arithmetic progression has a constant common difference of -5, and the geometric progression does not have a constant common ratio. Hence, the sequence is an arithmetic one

c

step-by-step explanation:

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.