Question

The sum of 3 numbers in GP is 42. If first two numbers are increased by 2 and third is decreases by 4 then resulting numbers form an A.P. Then the numbers of G.P. are –

• A. 3, 6, 12
• B. 6, 12, 24
• C. 4, 8, 16
• D. None

Answer 1

Answer: (B)

6, 12, 24

Answer 2

a + ar + ar² = 42 …(1)

a + 2, ar + 2, ar² – 4 form an A.P.

̃ 2 (ar + 2) = (a + 2) + (ar² – 4)

2ar + 4 = a + ar² – 2

a – 2ar + ar² = 6 …(2)

Divide (1) by (2)

= $\frac { 42 } { 6 }$

1 + r+ r² = 7 – 14 r + 7r²

6r² – 15r + 6 = 0

2r² – 5r + 2 = 0

̃ r = 2, $\frac { 1 } { 2 }$

when r = 2 ̃ a = 6

̃ 6, 12, 24

when r = $\frac { 1 } { 2 }$ ̃ a = 24

̃ 24, 12, 6