Question

The fourth term and the eighth term of a geometric

progression are 3 and 1/27 respectively. Find the

12th term.

(A) 1/243 (B) 1/729 (C) 1/2187 (D) 1/6561 ​

Answer 1

Answer:

1/2187

Step-by-step explanation:

Let the first term of the GP be 'a' and the common ratio be 'r'.

4th term = ar⁴⁻¹ = ar³

        ∴  3 = ar³             ...(1)

8th term = ar⁸⁻¹ = ar⁷

        ∴ 1/27 = ar⁷         ...(2)

On dividing (2) by (1), we get

⇒ 1/81 = r⁴

⇒ (1/3)⁴ = r⁴

⇒ 1/3 = r

     Substituting r in (1),

        ⇒ 3 = a(1/3)³     ⇒ 3⁴ = a

Hence the 12th term of the GP is:

        ⇒ ar¹²⁻¹

        ⇒ (3⁴)(1/3)¹¹

        ⇒ 1/3⁷

        ⇒ 1/2187

Answer 2

Answer:

Option C) 1/2187

Step-by-step explanation:

Check the solution from the attached photo.