Question

The product of three consecutive terms of a G. P. is 5832 and their sum is 57. Find the three terms​

Answer 1

Solution :-

Let us assume that three terms in GP are a, ar and ar² .

So,

→ a * ar * ar² = 5832

→ a³ * r³ = 5832

→ (ar)³ = 5832

→ (ar)³ = (18)³

→ ar = 18 ----- Equation (1)

and,

→ a + ar + ar² = 57

→ a + ar² = 57 - 18

→ a + ar² = 39

→ a + ar * r = 39

→ a + 18r = 39

→ a = (39 - 18r)

putting value of a in Equation (1),

→ (39 - 18r) * r = 18

→ 18r² - 39r + 18 = 0

→ 6r² - 13r + 6 = 0

→ 6r² - 9r - 4r + 6 = 0

→ 3r(2r - 3) - 2(2r - 3) = 0

→ (2r - 3)(3r - 2) = 0

→ r = (3/2) and (2/3)

when r = (3/2)

→ a * (3/2) = 18

→ a = 12

then three terms are :-

• a = 12
• ar = 18
• ar² = 27

and, when r = (2/3)

→ a * (2/3) = 18

→ a = 27

then three terms are :-

• a = 27
• ar = 18
• ar² = 12

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