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DIRECTIONS for the question:
Solve the following question and mark the best possible option.
The third, fifth and eighth terms of an A.P are consecutive terms of a G.P. The common ratio of the G.P will be :
  • a)
    2.5
  • b)
    3.5
  • c)
    0.5
  • d)
    1.5
Correct answer is option 'D'. Can you explain this answer?
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DIRECTIONS for the question: Solve the following question and mark the...
Let the A.P be a, a +d, a + 2d, …….
Then we have  (a + 4d)2 = (a +2d) (a +7d)….. (1)
or a = 2d.
Now common ratio = (a + 4d) / (a + 2d) = 6 / 4 = 1.5
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Most Upvoted Answer
DIRECTIONS for the question: Solve the following question and mark the...
Given:
- The third, fifth, and eighth terms of an arithmetic progression (A.P) are consecutive terms of a geometric progression (G.P).

To find:
- The common ratio of the G.P.

Solution:

Let's assume that the common difference of the arithmetic progression is 'd' and the common ratio of the geometric progression is 'r'.

Identify the terms:
- The third term of the A.P is 'a + 2d'.
- The fifth term of the A.P is 'a + 4d'.
- The eighth term of the A.P is 'a + 7d'.

Identify the terms of the G.P:
Since the third, fifth, and eighth terms of the A.P are consecutive terms of the G.P, we can write:
(a + 2d) * r = (a + 4d)
(a + 4d) * r = (a + 7d)

Solve the equations:
Expanding the equations, we get:
ar + 2dr = a + 4d
ar + 4dr = a + 7d

Subtracting the first equation from the second equation, we get:
2dr = 3d

Dividing both sides by 'd', we get:
2r = 3

Calculate the common ratio:
Dividing both sides by 2, we get:
r = 3/2 = 1.5

Therefore, the common ratio of the G.P is 1.5.

Conclusion:
The correct answer is option 'D' (1.5).
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DIRECTIONS for the question: Solve the following question and mark the best possible option.The third, fifth and eighth terms of an A.P are consecutive terms of a G.P. The common ratio of the G.P will be :a)2.5b)3.5c)0.5d)1.5Correct answer is option 'D'. Can you explain this answer?
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