#### Question

Let a_n be the general term of an arithmetic sequence, where the common difference is a non-zero constant. It is given that a_1 + a_3 + a_7 = 1 and a^2_2+a^2_3 =a^2_4+a^2_5

Find the general term an of the sequence.

If \dfrac{a_ma_{m+1}}{a_{m+2}} is a term of the sequence, how many possible values of m are there? Explain your answer.