Describe the pattern, write the next term, and write a rule for the $$ n $$th term of the sequence. $$ 2,9,28,65, \ldots $$ The pattern is The next term is The $$ n $$th term is $$ a_{n}= $$

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**Step 1:** Recognize that each term in the sequence can be written as the cube of its position in the sequence plus 1.

- For the 1st term: $$ 1^3 + 1 = 1 + 1 = 2 $$.  
- For the 2nd term: $$ 2^3 + 1 = 8 + 1 = 9 $$.  
- For the 3rd term: $$ 3^3 + 1 = 27 + 1 = 28 $$.  
- For the 4th term: $$ 4^3 + 1 = 64 + 1 = 65 $$.

**Step 2:** The next term would be the 5th term. Compute it using the rule:

$$
5^3 + 1 = 125 + 1 = 126
$$

**Step 3:** The rule for the $$ n $$th term is:

$$
a_n = n^3 + 1
$$

Thus, the pattern is that each term is the cube of its index plus 1, the next term is 126, and the $$ n $$th term is given by $$ a_{n} = n^3 + 1 $$.
**Pattern:** Each term is the cube of its position plus 1. **Next Term:** 126 **Rule for the $$ n $$th Term:** $$ a_{n} = n^3 + 1 $$

Describe the pattern, write the next term, and write a rule for the \( n \)th term of the sequence. \( 2,9,28,65, \ldots \) The pattern is The next term is The \( n \)th term is \( a_{n}= \)

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