Answer:
Options 1, 3 and 4.
Step-by-step explanation:
As we know in an arithmetic sequence each successive term has a common difference.
Let's check each option for Arithmetic sequence.
Option 1.
-8.6, -5.0, -1.4, 2.2, 5.8,....
Difference between 2nd and 1st term
-5 - (-8.6) = -5 + 8.6
= 3.6
Difference between 4th and 3rd term
-1.4 - (-5) = -1.4 + 5
= 3.6
This proves that there is a common difference of 3.6 which shows that the sequence is an arithmetic sequence.
Option 2.
2, -2.2, 2.42, -2.662, 2.9282,....
2nd term - 1st term = (-2.2) - 2 = -4.2
3rd term - 2nd term = 2.42 - (-2.2) = 2.42 + 2.2 = 4.62
Here difference in each term of the sequence is not common so it's not an arithmetic sequence.
Option 3.
5, 1, -3, -7, -11,.......
2nd term - 1st term = 1 - 5 = -4
3rd term - 2nd term = -3 - 1 = -4
Therefore, the given sequence is an arithmetic sequence.
Option 4.
-3, 3, 9, 15, 21,.......
2nd term - 1st term = 3 - (-3) = 3+ 3 = 6
3rd term - 2nd term = 9 - 3 = 6
There is a common difference of 6 in each term so it's an arithmetic sequence.
Option 5.
-6.2, -3.1, -1.55, -0.775, -0.3875,.........
2nd term - 1st term = -3.1 - (-6.2) = 6.2 - 3.1 = 3.1
3rd term - 2nd term = -1.55 - (-3.1) = 3.1 - 1.55 = 1.55
And 3.1 ≠ 1.55 which shows that this sequence is not an arithmetic sequence.
Options 1, 3 and 4 are arithmetic sequences.
, so this is rational as well.