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Algorithms Quiz | SP2 Contest 1 | Question 40
  • Last Updated : 03 Nov, 2020

The sum of the first three consecutive numbers in a GP is 104 and their product is 13824. Find the difference between the third and second number.

(A) 48
(B) 64
(C) 32
(D) 52


Answer: (A)

Explanation: Let the numbers be a/r, a, ar
=> (a / r) + a + a r = 104
=> a (1 + r + r2) / r = 104
Also, it is given that product = 13824
=> (a / r) x (a) x (a r) = 13824
=> a3 = 13824
=> a = 24
=> 24 (1 + r + r2) / r = 104
=> (1 + r + r2) / r = 104 / 24
On solving this equation we get r = 3,
Therefore, the three numbers are: 8, 24 and 72.
So, difference of third and second number is:

72 - 24 = 48 

So, option (A) is correct.

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