Which sequences are arithmetic? Select three options. -8.6, -5.0, −1.4, 2.2, 5.8, ... 2, −2.2, 2.42, -2.662, 2.9282, ... 5, 1, −3, −7, −11, ... -3, 3, 9, 15, 21, ... -6.2, −3.1, −1.55, −0.775, −0.3875, ...

To solve the problem we must know about Arithmetic Sequence.Arithmetic SequenceAn arithmetic sequence is a sequence in which the difference between any two terms of the sequence is the same or equal.[tex]a_n = a_1 + (n-1)r[/tex]where,[tex]a_n[/tex] is the nth term of the sequence,[tex]a_1[/tex] is the first term of the sequence,r is a common difference between every two terms.The options that are arithmetic sequences are A, C, and D.ExplanationGiven optionsA.)   -8. 6, –5. 0, –1. 4, 2. 2, 5. 8, …B.)   2, –2. 2, 2. 42, –2. 662, 2. 9282, …C.)   5, 1, –3, –7, –11, … D.)   –3, 3, 9, 15, 21, … E.)   –6. 2, –3. 1, –1. 55, –0. 775, –0. 3875, ….A.)   -8. 6, –5. 0, –1. 4, 2. 2, 5. 8, …[tex]a_1 = -8.6\\ a_2 = -5.0\\ a_3 = -1.4\\ a_4 = 2.2\\ a_5 = 5.8[/tex]We know that for a series to be an arithmetic Sequence. the difference between any two consecutive terms should be equal.[tex]a_1 - a_2= -8.6 - (-5.0) = -3.6\\ a_2 -a_3= -5.0 - (-1.4)= -3.6\\ a_3 -a_4= -1.4-2.2 = -3.6[/tex]Hence, the series is an arithmetic Sequence.B.)   2, –2. 2, 2. 42, –2. 662, 2. 9282, …[tex]a_1 = 2\\ a_2 = -2.2\\ a_3 = 2.42\\ a_4 = -2.662\\ a_5 = 2.9282[/tex]We know that for a series to be an arithmetic Sequence. the difference between any two consecutive terms should be equal.[tex]a_1 - a_2= 2- (-2.2) = 4.2\\ a_2 -a_3= -2.2- (2.42)= 0.22\\ [/tex]Hence, the series is not an arithmetic Sequence.C.)   5, 1, –3, –7, –11, … [tex]a_1 = 5\\ a_2 = 1\\ a_3 = -3\\ a_4 = -7\\ a_5 = -11[/tex]We know that for a series to be an arithmetic Sequence. the difference between any two consecutive terms should be equal.[tex]a_1 - a_2= -4\\ a_2 -a_3= -4\\ a_3 -a_4= -4[/tex]Hence, the series is an arithmetic Sequence.D.)   –3, 3, 9, 15, 21, … [tex]a_1 = -3\\ a_2 = 3\\ a_3 = 9\\ a_4 = 15\\ a_5 = 21[/tex]We know that for a series to be an arithmetic Sequence. the difference between any two consecutive terms should be equal.[tex]a_1 - a_2= 6\\ a_2 -a_3= 6\\ a_3 -a_4= 6[/tex]Hence, the series is an arithmetic Sequence.E.)   –6. 2, –3. 1, –1. 55, –0. 775, –0. 3875, ….[tex]a_1 = -6.2\\ a_2 = -3.1\\ a_3 = -1.55\\ a_4 = -0.775\\ a_5 = -0.3875[/tex]We know that for a series to be an arithmetic Sequence. the difference between any two consecutive terms should be equal.[tex]a_1 - a_2= -6.2- (-3.1) = -3.1\\ a_2 -a_3= -3.1- (-1.55)= -1.55\\ [/tex]Hence, the series is not an arithmetic Sequence.Hence, the options that are arithmetic sequences are A, C, and D.Learn more about Arithmetic Sequence: