#### Question

Let a_n be the n-th term of an arithmetic sequence, where the common difference is a non-zero constant. It is given that a_1 + a_3 + a_5 =\dfrac{72}{5} and a^2_1= a^2_{11}

Express a_n in terms of n.

Find the first negative term of the sequence.

Elaine claims that there exists a positive integer h such that 5a_h = h^2. Do you agree? Explain your answer.