Question

Solve previous year Question of iit jee

Chapter :- sequence and series​

Answer 1

Answer:

Common ratio of GP is 4/3 , option (b) is correct .

Step-by-step explanation:

Let a be the first term and d be the common difference . then ,we have

• a₂ = a+d
• a₅ = a+4d
• a₉ = a + 8d

So as we know that ,if a , b and c are in GP then

b² = ac [Property of GP]

(a+4d)² = (a+d) (a+8d)

→a² + 16d² + 8ad = a² + 8ad

→8d² = ad

→ 8d = a _______(i)

Now , common ratio ,

• r = a+4d /a+d
• → 8d +4d/8d+d
• → 12d/9d = 4/3Answer

Answer 2

EXPLANATION.

2nd, 5th and 9th term of a non- constant A.P. are in G.P.

As we know that,

⇒ 2nd term = a + d.

⇒ 5th term = a + 4d.

⇒ 9th term = a + 8d.

⇒ a + d, a + 4d, a + 8d. - - - - - (G.P.).

As we know that,

Conditions of a G.P.

⇒ b² = ac.

Put the values in the equation, we get.

⇒ (a + 4d)² = (a + d)(a + 8d).

⇒ a² + 16d² + 8ad = a² + 8ad + ad + 8d².

⇒ a² + 16d² + 8ad = a² + 9ad + 8d².

⇒ a² + 16d² + 8ad - a² - 9ad - 8d² = 0.

⇒ 16d² - 8d² + 8ad - 9ad = 0.

⇒ 8d² - ad = 0.

⇒ d(8d - a) = 0.

⇒ 8d = a.

Common ratios = r = b/a.

⇒ r = (a + 4d)/(a + d).

⇒ r = (8d + 4d)/(8d + a).

⇒ r = 12d/9d = 4/3.

Option [B] is correct answer.