Q&A If the sequence \{a_n\} has its first term a_1=1, a_{n+1}=\dfrac{1+4a_n+\sqrt{1+24a_n}}{16} , find the formula for general terms of the sequence.

Q&A Show that the sequence \{a_n\} is composed of terms of integers if a_0=1 and a_{n+1}=\dfrac{3a_n+\sqrt{5a^2_n-4} }{2}

Q&A Given the sequence series \{a_n\} satisfies a_1=1 , a_2=\dfrac{2}{3} and \dfrac{1}{a_{n+1}} +\dfrac{1}{a_{n-1}}=\dfrac{2}{a_n} (n=2,3,\dots) , find the general term of a_n

Q&A If a sequence has a first term of a_1=10 , and a common difference d=5 , Write the formula that describes this sequence. Use the formula of the arithmetic sequence.