What is the common difference in the following arithmetic sequence? n an, 1 –12, 2 –1, 3 10, 4 21. Explain step by step in detail.

What is the common difference in the following arithmetic sequence? n an 1 –12 2 –1 3 10 4 21 –11 –1 1 11

To find the common difference ($�$) in an arithmetic sequence, you can subtract the first term from the second term (or any subsequent term) in the sequence. Here's how you can do it step by step for the given sequence:

The sequence is: $�$ ${�}_{�}$ 1 -12 2 -1 3 10 4 21

Let's find the common difference by subtracting the first term from the second term:

Subtract the second term from the first term: $-1-(-12)=-1+12=11$

So, the common difference between the first and second terms is 11.

Now, let's verify that the common difference is the same for the other terms in the sequence by subtracting consecutive terms:

Subtract the third term from the second term: $10-(-1)=10+1=11$

Subtract the fourth term from the third term: $21-10=11$

The common difference ($�$) between consecutive terms in this arithmetic sequence is consistently 11.

Therefore, the common difference in the sequence is 11.