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Three numbers in geometric progression have a sum of 42 and a product of 512. Find the numbers.
1. 2, 8, 32
2. 1, 4, 16
3. 3, 6, 12
4. 3, 12, 48
5. 4, 16, 64

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Correct Answer - Option 1 : 2, 8, 32

Calculation:

Let the numbers be a/r, a and ar.

a/r+ a + ar = 42

(a/r) × a × (ar) = 512

⇒ a3 = 512

⇒ a = 8

⇒ 8/r + 8 + 8r = 42

⇒ 8 + 8r + 8r2 = 42r

⇒ 8r2 - 34r + 8 = 0

⇒ 8r2 - 32r - 2r + 8 = 0

⇒ 8r(r - 4) -2(r - 4) = 0

⇒ (r − 4) × (8r − 2) = 0

⇒ (r − 4) × (4r − 1) = 0
⇒ r = 4 or 1/4

⇒ Numbers 2, 8, 32

When there are three terms in geometric progression, we can represent the three terms be a/r, a, and ar

When there are four terms in geometric progression, we can represent the four terms as a/r3, a/r, ar, ar3

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