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There are four numbers of which the first three are in G.P. and the last three are in A.P., whose common difference is 6. If the first and the last numbers are equal then two other numbers are
  • a)
    –2, 4
  • b)
    –4,  2
  • c)
    2,  6
  • d)
    n on e
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
There are four numbers of which the first three are in G.P. and the la...
Let the last three numbers in A.P. be a, a + 6, a + 12, then the first term is also a + 12.
But  a + 12, a, a + 6 are in G.P.
∴ a 2 = (a +12) (a + 6) ⇒ a 2 = a 2 +18a + 72
∴ a  =  –4.
∴ The numbers are 8, –4, 2, 8.
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Most Upvoted Answer
There are four numbers of which the first three are in G.P. and the la...
Explanation:

Given Information:
- The first three numbers are in Geometric Progression (G.P.)
- The last three numbers are in Arithmetic Progression (A.P.) with a common difference of 6
- The first and last numbers are equal

Solution:
Let the common ratio of the Geometric Progression be 'r' and the first term be 'a'.
So, the three numbers in G.P. will be a, ar, ar^2.
Since the first and last numbers are equal, we have:
a = ar^2
From the given information, the common difference of the Arithmetic Progression is 6.
So, the three numbers in A.P. will be (ar^2), (ar^2 + 6), (ar^2 + 12).
Since the last three numbers are in A.P., we have:
(ar^2) + (ar^2 + 12) = 2(ar^2 + 6)
2ar^2 + 12 = 2ar^2 + 12
This equation is true for all values of r.
Now, let's check the given options:
a) -2, 4
If a = -2, then r = 1/2
The numbers in G.P. will be -2, -1, -1/2
The numbers in A.P. will be -1/2, 5/2, 11/2
The common difference is not 6.
b) -4, 2
If a = -4, then r = 1/2
The numbers in G.P. will be -4, -2, -1
The numbers in A.P. will be -1, 5, 11
The common difference is 6. This satisfies all conditions.
c) 2, 6
If a = 2, then r = 1/2
The numbers in G.P. will be 2, 1, 1/2
The numbers in A.P. will be 1/2, 7/2, 13/2
The common difference is not 6.
d) None
Option b) -4, 2 satisfies all the given conditions.
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There are four numbers of which the first three are in G.P. and the last three are in A.P., whose common difference is 6. If the first and the last numbers are equal then two other numbers area)–2, 4b)–4, 2c)2, 6d)n on eCorrect answer is option 'B'. Can you explain this answer?
Question Description
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