Question

If a, b, c are in H.P., b, c, d are in GP and c, d, e are in AP then value of e is –

• A. $\frac { a b ^ { 2 } } { ( 2 a - b ) ^ { 2 } }$
• B. $\frac { a ^ { 2 } b } { ( 2 a - b ) ^ { 2 } }$
• C. $\frac { a ^ { 2 } b ^ { 2 } } { ( 2 a - b ) ^ { 2 } }$
• D. None

Answer 1

Answer: (A)

$\frac { a b ^ { 2 } } { ( 2 a - b ) ^ { 2 } }$

Answer 2

a, b, c are in HP ̃ b = …(1)

b, c, d are in GP ̃ c² = bd …(2)

c, d, e are in AP ̃ d = …(3)

from (1) ab + bc = 2ac

̃ c ̃ …(4)

from (iii) and (iv)

d = $\frac { 1 } { 2 }$ …(5)

$\frac { a ^ { 2 } b ^ { 2 } } { ( 2 a - b ) ^ { 2 } }$=

̃ we get e = .