Answer:
Option B & C are correct.
Explanation:
To find: Arithmetic sequence
Option A).
54 , 71 , 88 , 102 , 122 , ...
here a = 54
difference of 1st and 2nd term = 71 - 54 = 17
difference of 2nd and 3rd term = 88 - 71 = 17
difference of 3rd and 4th term = 102 - 88 = 14
So, Differences are not common.
Thus, It is not a arithmetic sequence.
Option B).
45 , 46 , 47 , 48 , 49 , ...
here a = 45
difference of 1st and 2nd term = 46 - 45 = 1
difference of 2nd and 3rd term = 47 - 46 = 1
difference of 3rd and 4th term = 48 - 47 = 1
So, Differences are common.
Thus, It is a arithmetic sequence.
Option C).
3 , 10 , 17 , 24 , 31 , ...
here a = 3
difference of 1st and 2nd term = 10 - 3 = 7
difference of 2nd and 3rd term = 17 - 10 = 7
difference of 3rd and 4th term = 24 - 17 = 7
difference of 4th and 5th term = 31 - 24 = 7
So, Differences are common.
Thus, It is a arithmetic sequence.
Option D).
-3 , -11 , -17 , -23 , -33 , ...
here a = -3
difference of 1st and 2nd term = -11 - ( -3) = -8
difference of 2nd and 3rd term = -17 - ( -11) = -6
So, Differences are not common.
Thus, It is not a arithmetic sequence.
Option E).
1 , -2 , 3 , -4 , 5 , ...
here a = 1
difference of 1st and 2nd term = -2 - 1 = -3
difference of 2nd and 3rd term = 3 - (-2) = 5
So, Differences are not common.
Thus, It is not a arithmetic sequence.
Therefore, Option B & C are correct.