# How do you write a rule for the nth term of the arithmetic sequence #a_7=21, a_13=42#?

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To write a rule for the nth term of an arithmetic sequence, you need to first find the common difference ((d)) between consecutive terms. Once you have the common difference, you can use the formula for the nth term of an arithmetic sequence:

[a_n = a_1 + (n - 1) \times d]

Given that (a_7 = 21) and (a_{13} = 42), you can find the common difference by subtracting the two terms and dividing by the difference in their indices:

[d = \frac{a_{13} - a_7}{13 - 7}]

Once you have the common difference, you can use it to find the first term ((a_1)) by substituting any known term into the formula. Then, you can write the rule for the nth term using the formula above, where (a_n) represents the nth term, (a_1) is the first term, and (d) is the common difference.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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