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10 Apr 2021, 11:47
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Difficulty:
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Question Stats:
59% (01:59) correct
41%
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What number should be added to each of the three numbers -2, 5 and 20, so that the resulting three numbers form a geometric progression?
A. 8.125
B. 8
C. 7.875
D. 7.5
E. 7
A. 8.125
B. 8
C. 7.875
D. 7.5
E. 7
priyachandank
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10 Apr 2021, 12:59
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can someone post the steps to solve this, please? thank you in advance.
Updated on: 14 Jul 2021, 04:53
Originally posted by andreagonzalez2k on 10 Apr 2021, 13:34.
Last edited by andreagonzalez2k on 14 Jul 2021, 04:53, edited 2 times in total.
Last edited by andreagonzalez2k on 14 Jul 2021, 04:53, edited 2 times in total.
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Let 'a' be the number we have to add.
Let 'b' be the common ratio.
\((-2 + a) b = 5 + a\)
\((-2 + a) b^2 = 20 + a\)
From the first equation:
\(a = \frac{(2b + 5)}{(b-1)}\)
From the second equation
\(a = \frac{(2b^2 + 20)}{((b-1)(b+1))}\)
Solving we have
\(b = \frac{15}{7}\)
\(a = 8.125\)
The terms of the geometric progression are 6.125, 13.125, 28.125
Let 'b' be the common ratio.
\((-2 + a) b = 5 + a\)
\((-2 + a) b^2 = 20 + a\)
From the first equation:
\(a = \frac{(2b + 5)}{(b-1)}\)
From the second equation
\(a = \frac{(2b^2 + 20)}{((b-1)(b+1))}\)
Solving we have
\(b = \frac{15}{7}\)
\(a = 8.125\)
The terms of the geometric progression are 6.125, 13.125, 28.125
