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Find a formula for the nth term following the sequence.

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Final answer:

The formula for the nth term in the sequence is n², which can be derived by adding (n-1) from the last term to the first term and simplifying the expression.

Step-by-step explanation:

The formula for the nth term in the sequence is n². To derive this formula, imagine taking (n-1) from the last term and adding it to the first term. This gives us 2[1+(n-1)+3+...+(2n-3)+(2n-1)-(n-1)]. Simplifying further, we get 2[n+3+....+(2n-3)+n]. Now, take (n-3) from the penultimate term and add it to the second term. This gives us 2[n+n+....+n+n], which simplifies to 2n².

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