1. **State the problem:** We are given the nth term of a sequence as $$T(n) = 3n^2 + 8$$ and told that a term in this sequence has a value of 83. We need to find the position $$n$$ of this term. 2. **Write the equation:** Set $$T(n) = 83$$: $$3n^2 + 8 = 83$$ 3. **Solve for $$n$$:** Subtract 8 from both sides: $$3n^2 = 83 - 8$$ $$3n^2 = 75$$ Divide both sides by 3: $$n^2 = \frac{75}{3} = 25$$ 4. **Find $$n$$:** Take the square root of both sides: $$n = \pm 5$$ 5. **Interpret the result:** Since $$n$$ represents the position in the sequence, it must be a positive integer. Therefore, $$n = 5$$. **Final answer:** The term with value 83 is at position $$n = 5$$.