Find the Domain an=(n(6n+5))/2

Problem

(a_n)=(n*(6*n+5))/2

Solution

1. Identify the type of expression provided. The expression (a_n) represents a sequence, where n typically denotes the position of a term within that sequence.

2. Determine the standard set of inputs for sequences. In mathematics, the domain of a sequence consists of the set of natural numbers or positive integers.

3. Check for any algebraic restrictions. The expression (n*(6*n+5))/2 is a polynomial in n divided by a constant. There are no values of n that would result in division by zero or the square root of a negative number.

4. Define the domain based on sequence conventions. Unless otherwise specified, the domain is the set of all positive integers {1,2,3,…}

Final Answer

Domain={[n∈ℤ,n≥1]}

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