Q&A Given a geometric sequence with the common ratio q (q>1) and the number of terms m, removing one of the terms from the sequence will result in a new sequence. Find the values of m and q if the new sequence is an arithmetic sequence. Arithmetic sequence

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. Recursive 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} Recursive Sequence

Q&A If a, b, c are three sides of the \triangle ABC and A, B, C are their corresponding vertex, show that a^2\tan\dfrac{A}{2}+b^2\tan\dfrac{B} {2}+c^2\tan\dfrac{C}{2}\geq 4S in which S is the area of the triangle. Trigonometry