Question

The product of first three terms of a G. P. is 512. If we add 2 to its second term, the three terms form an A. P. Find the terms of the G. P.

Answer 1

Step-by-step explanation:

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Answer 2

let first three terms of a G.P is a/r, a, ar.

a/c to question,

product of first three terms = 512

⇒ a/r × a × ar = 512

⇒a³ = 512 = (8)³

⇒a = 8

hence, second term , a = 8

2 is added to its second term, then three terms form an A.P

means, 8/r, (8 + 2), 8r are in A.P

we know, common difference remains same for A.P

so, (8 + 2) - 8/r = 8r - (8 + 2)

⇒ 10 - 8/r = 8r - 10

⇒ 10 + 10 = 8r + 8/r

⇒ 20r = 8r² + 8

⇒5r = 2r² + 2

⇒2r² - 5r + 2 = 0

⇒2r² - 4r - r + 2 = 0

⇒2r(r - 2) -(r - 2) = 0

⇒(2r - 1)(r - 2) = 0

⇒ r = 2, 1/2

now, G.P terms are ; 8/(2), 8, 8(2) [ taking r = 2 ]

⇒hence, G.P terms are ; 4, 8, 16