Which of the following sequences of numbers are arithmetic sequences?

Option B & C are correct.

Step-by-step 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.

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step-by-step explanation: