Question

a,b,c are in G.P as well as A.P .
Show that a= b=c

Answer 1

a, b, c are in GP as well as AP
if a, b, c are in GP then,
b² = ac { common ratio is constant}
and if are in AP then,
b = (a + c)/2 { common difference is constant}

(a + c)²/4 = ac
a² + c² + 2ac = 4ac
a² + c² -2ac = 0
(a - c)² = 0
a - c = 0
a = c
now put it , b = (a + c)/2
b = (a + a)/2 = (c + c )/2
b = a = c
a = b = c
hence proved //