Determine if the sequence is arithmetic or geometric, and find the common difference or ratio. x 1 2 3 4
f(x) 5 −5 −15 −25
Arithmetic, common difference = −10
Arithmetic, common difference = −1
Geometric, common ratio = −10
Geometric, common ratio = −1

The correct option is;

Arithmetic, common difference = -10

Step-by-step explanation:

The x terms given of the sequence are;

x          1          2         3         4      

f(x)         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.

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