which sequences are arithmetic? select three options. -8.6, -5.0, -1.4, 2.2, 5.8, ... 2, -2.2, 2.42, -2.662…

Explanation:

Step1: Recall arithmetic - sequence definition

An arithmetic sequence has a common difference (d) between consecutive terms, where (d=a_{n + 1}-a_{n}).

Step2: Check the first sequence (-8.6,-5.0,-1.4,2.2,5.8,\cdots)

(d=-5.0-( - 8.6)=3.6), (-1.4-( - 5.0)=3.6), (2.2-( - 1.4)=3.6), (5.8 - 2.2=3.6). It is an arithmetic sequence.

Step3: Check the second sequence (2,-2.2,2.42,-2.662,2.9282,\cdots)

(\frac{-2.2}{2}=-1.1), (\frac{2.42}{-2.2}=-1.1). It is a geometric sequence (not arithmetic) since there is a common - ratio, not a common difference.

Step4: Check the third sequence (5,1,-3,-7,-11,\cdots)

(d = 1 - 5=-4), (-3 - 1=-4), (-7-( - 3)=-4), (-11-( - 7)=-4). It is an arithmetic sequence.

Step5: Check the fourth sequence (-3,3,9,15,21,\cdots)

(d=3-( - 3)=6), (9 - 3=6), (15 - 9=6), (21 - 15=6). It is an arithmetic sequence.

Step6: Check the fifth sequence (-6.2,-3.1,-1.55,-0.775,-0.3875,\cdots)

(\frac{-3.1}{-6.2}=0.5), (\frac{-1.55}{-3.1}=0.5). It is a geometric sequence (not arithmetic) since there is a common - ratio, not a common difference.

Answer:

-8.6, -5.0, -1.4, 2.2, 5.8, ... 5, 1, -3, -7, -11, ... -3, 3, 9, 15, 21, ...