Question

Q= 1 ‐ a / b ÷ 1 ‐ c / b = ?​

Answer 1

We know foe any n

th

term of an A.P, n

th

term =a+(n−1)d where a= first term and d= common difference.

∴ a

1

+(p−1)d=

a

1

,

a

1

+(9−1)d=

h

1

and a

1

+(r−1)d=

c

1

∴

a

1

=(a

1

−d)+pd−−−(1),

b

1

=(a

1

−d)+qd−−−(2) and

c

1

=(a

1

−d)+rd−−−(3)

By (1)−(2),(2)−(3) and (3)−(1)

a

1

−

b

1

=(p−q)d,

b

1

,

c

1

=(q−r)d and

c

1

−

a

1

=(r−p)d

∴

d(ab)

b−a

=p−q,

d(bc)

c−b

=q−r,

d(ac)

a−c

=r−p

or,

d

b−a

=ab(p−q),

d

c−b

=bc(q−r),

d

a−c

=ac(r−p)

Adding all the equation

d

(b−a)+(c−b)+(a−c)

=ab(p−q)+bc(q−r)+ac(r−p)

or, ab(p−q)+bc(q−r)+ac(r−p)=0------Proved,