Question

The product of first three terms of G.P is 1000. If 6 is added to its second term and
7 is added to its third term, the terms become in A.P. Find G.P
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Answer 1

Answer:

The product of first three terms of G.P is 1000. If 6 is added to its second term and

7 is added to its third term, the terms become in A.P. Find G.P

PLEASE WRITE STEP BY STEP

Answer 2

GiveN:

The product of first three terms of a G.P is 1000.

1000.If 6 is added to its second term and 7 added to its third term, the terms form in AP.

To FinD:

• The GP?

Step-by-step Explanation:

We have the three terms in GP.

Let the terms be a/r, a, ar

According to question,

⇒ a/r × a × ar = 1000

⇒ a³ = 1000

⇒ a³ = 10³

⇒ a = 10

Now it is given that when 6 is added to its second term and 7 added to its third term, the terms form in AP.

• The second term will be a + 6
• And third term will be ar + 7
• And we know that when the terms form in AP,

2(Second term) = First term + Third term

Plugging the given values:

⇒ 2(a + 6) = a/r + ar + 7

⇒ 2(10 + 6) = 10/r + 10r + 7

⇒ 32 = 10/r + 10r + 7

⇒ 10/r + 10r = 25

⇒ 10 + 10r² / r = 25

⇒ 10r² + 10 = 25r

⇒ 2r² - 5r + 2 = 0

Finding values of r by middle term factorisation,

⇒ 2r² - 4r - r + 2 = 0

⇒ 2r(r - 2) - 1(r - 2) = 0

⇒ (2r - 1)(r - 2) = 0

⇒ Then, r = 1/2 , 2

Hence,

The numbers are 5,10,20 / 20,10,5.