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The sum of 3 numbers of a G P is 39 and their product is 729. The numbers are
- a)3, 27, 9
- b)9, 3, 27
- c)3, 9, 27
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The sum of 3 numbers of a G P is 39 and their product is 729. The numb...
Option (C) is correct
39 = ar + ar^2 + ar^3
39 = ar + ar^2 + ar^3
729 = (ar) * (ar^2) * (ar^3)
729 = (ar) * (ar^2) * (ar^3)
729 = (ar)^3 * r^3
9^3 = (ar)^3 * r^3
9 = ar * r
9 = ar^2
39 = ar + ar^2 + ar^3
39 = ar^2 / r + ar^2 + ar^2 * r
39 = 9/r + 9 + 9r
13 = 3/r + 3 + 3r
13r = 3 + 3r + 3r^2
0 = 3 - 10r + 3r^2
r = (10 +/- sqrt(100 - 36)) / 6
r = (10 +/- 8) / 6
r = 18/6 , 2/6
r = 3 , 1/3
ar^2 = 9
a * 3^2 , a * (1/3)^2 = 9
a * 9 , a * (1/9) = 9
a = 1 , 81
If r = 3, then:
ar , ar^2 , ar^3 =>
1 * 3 , 1 * 3^2 , 1 * 3^3 =>
3 , 9 , 27
If r = 1/3, then:
ar , ar^2 + ar^3 =>
81 / 3 , 81 / 9 , 81 / 27 =>
27 , 9 , 3
Either way, the 3 numbers are 3 , 9 , and 27.
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Community Answer
The sum of 3 numbers of a G P is 39 and their product is 729. The numb...
Given:
The sum of 3 numbers of a G P is 39 and their product is 729.
To find:
The three numbers in the G P.
Solution:
Let the three numbers be a, ar and ar^2.
According to the given condition,
a + ar + ar^2 = 39 ...(1)
a × ar × ar^2 = 729
a^3 r^3 = 729
ar = 9 ...(2)
Substituting (2) in (1),
a + 9 + 9r = 39
a + 9r = 30 ...(3)
Substituting (2) in (3),
a + (a/9)×9 = 30
a + a = 30
2a = 30
a = 15
Substituting a = 15 in (2),
ar = 9
r = 9/15 = 3/5
Therefore, the three numbers in the G P are:
a = 15, ar = 9 and ar^2 = 27/5
Hence, option (c) 3, 9, 27 is the correct answer.
The sum of 3 numbers of a G P is 39 and their product is 729.
To find:
The three numbers in the G P.
Solution:
Let the three numbers be a, ar and ar^2.
According to the given condition,
a + ar + ar^2 = 39 ...(1)
a × ar × ar^2 = 729
a^3 r^3 = 729
ar = 9 ...(2)
Substituting (2) in (1),
a + 9 + 9r = 39
a + 9r = 30 ...(3)
Substituting (2) in (3),
a + (a/9)×9 = 30
a + a = 30
2a = 30
a = 15
Substituting a = 15 in (2),
ar = 9
r = 9/15 = 3/5
Therefore, the three numbers in the G P are:
a = 15, ar = 9 and ar^2 = 27/5
Hence, option (c) 3, 9, 27 is the correct answer.
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