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Explicate rule for the sequence,
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Q. Explicate rule for the sequence,
- Identify Differences: To find the rule for the sequence, we first look at the differences between consecutive terms to see if there is a pattern.The differences are:
- Recognize Odd Number Pattern: We notice that the differences between consecutive terms are odd numbers and they are increasing by each time. This suggests that the sequence is generated by adding consecutive odd numbers to the previous term, starting with .
- Write Sequence in Terms: To confirm the pattern, we can write the sequence in terms of the first term and the sum of the odd numbers:This confirms that the rule involves adding consecutive odd numbers starting from to the first term, which is .
- Express nth Term Formula: The th term of the sequence can be expressed as the sum of the first term () and the sum of the first () odd numbers starting from . The sum of the first () odd numbers is , since the sum of the first odd numbers is .Therefore, the th term of the sequence is given by:nth term =
