Subjects algebra

Arithmetic Sequence 9F9A95

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1. The problem is to find the rule or pattern for the sequence: 20, 30, 40, 50, 60. 2. To find the rule, observe the differences between consecutive terms: $$30 - 20 = 10$$ $$40 - 30 = 10$$ $$50 - 40 = 10$$ $$60 - 50 = 10$$ 3. Since the difference between each term is constant (10), this is an arithmetic sequence. 4. The general formula for an arithmetic sequence is: $$a_n = a_1 + (n-1)d$$ where $a_n$ is the $n$th term, $a_1$ is the first term, and $d$ is the common difference. 5. Here, $a_1 = 20$ and $d = 10$, so: $$a_n = 20 + (n-1) \times 10$$ 6. Simplify the formula: $$a_n = 20 + 10n - 10 = 10n + 10$$ 7. Therefore, the rule for the sequence is: $$a_n = 10n + 10$$ This means to find the $n$th term, multiply $n$ by 10 and add 10.