Determine if the sequence is arithmetic or geometric, and find the common difference or ratio. х

1

2.

3

4

f(x) 81 72 63 54

O Arithmetic, common difference = 9

Arithmetic, common difference = -9

Geometric, common ratio = 9

O Geometric, common ratio = -9

A

Step-by-step explanation:

arithmatic

The correct option is;

Arithmetic, common difference = -10

Step-by-step explanation:

The x terms given of the sequence are;

x [tex]{}[/tex] 1 2 3 4

f(x) [tex]{}[/tex] 5 -5 -15 -25

For a geometric progression, a·r/a = a·r²/ar = ar³/ar² = (n + 1)/n = r

We check to obtain -5/5 ≠ -15/(-5), therefore, the system is not a geometric progression

For ab arithmetic progression, we have;

(n + 1)th term - nth term = (n + 2)th term - (n + 1)th term = d (The common difference

We check to obtain -5 - 5 10, -15 - (-5) = -15 + 5 = -10 similarly, we have; -25 - (-15) = -25 + 15 = -10

Therefore, the sequence is an arithmetic sequence, with common difference = -10.

The sequence is arithmetic with a common difference of -10

Step-by-step explanation:

From the question, we want to determine if the sequence is arithmetic or geometric

From the question

f(1) = 5

f(2) = -5

f(3) = -15

Mathematically for the common difference;

f(3) - f(2) = f(2) - f(1)

Since;

-15-(-5) = -5-5

-10 = -10

Since the common difference here is same , then the sequence is arithmetic with a common difference of -10

option 1 A)arithmetic,common difference= -10

Step-by-step explanation:

i took the test and got the answer correct

arthimetic 9

Step-by-step explanation:

Geometric, common ratio = 3

Step-by-step explanation:

Took test

(Please give me brainiest so I can move to the next level)

C. Geometric, common ratio = 3

Step-by-step explanation:

Got it right

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