2021/020) If a,b,c are three successive terms of an A.P., then prove that$ a^2+8bc=(2b+c)^2$

Because a, b, c are 3  successive terms of an A.P. so we have

b- a = c- b or a = 2b - c

now LHS = $a^2 + 8bc = (2b-c)^2 + 8bc = 4b^2 - 4bc + c^2 + 8bc = 4b^2 + 4bc + c^2 = (2b+c)^2$