which sequences are arithmetic? select three options.\n□ - 8.6, - 5.0, - 1.4, 2.2, 5.8, ...\n□ 2, - 2.2…

Explanation:

Step1: Recall arithmetic - sequence formula

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

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

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

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

(d=-2.2 - 2=-4.2), (2.42-( - 2.2)=2.42 + 2.2 = 4.62). Since the differences are not the same, it is not an arithmetic sequence.

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

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

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

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

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

(d=-3.1-( - 6.2)=-3.1 + 6.2 = 3.1), (-1.55-( - 3.1)=-1.55 + 3.1 = 1.55). Since the differences are not the same, it is not an arithmetic sequence.

Answer:

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