Question

if a, b, c are in G. P. and a, x, b, y, c are in A. P., prove that :
(I)
$\frac{1}{x} + \frac{1}{y} = \frac{2}{b}$
(ii)
$\frac{a}{x} + \frac{c}{y} = 2$
plz tell fast...

Answer 1

fb.b = ac

let d be common difference of Ap
x = a+d
b = a+2d
y = a+3d
c= a + 4d

(a+2d)^2 = a(a+4d)

a^2 + 4d.d + 4da= a^2 + 4da

4d^2=0
d=0

so all are equal

1/x + 1/y
x= y = b

1/b + 1/b =2/b

2)a/x + c/y = 1+1 =2