Question

3. Find six geometric means between
1/81
and 27.​

Answer 1

Answer:

Let the six terms be a1, a2, a3, a4, a5, a6. A = 27, B = 1/81 Now, these 6 terms are between A and B. So the GP is: A, a1, a2, a3, a4, a5, a6, B. So we now have 8 terms in GP with the first term being 27 and eighth being 1/81. We know that, Tn = arn–1 Here, Tn = 1/81, a = 27 and 1/81 = 27r8-1 1/(81 × 27) = r7 r = 1/3 a1 = Ar = 27 × 1/3 = 9   a2 = Ar2 = 27 × 1/9 = 3    a3 = Ar3 = 27 × 1/27 = 1    a4 = Ar4 = 27 × 1/81 = 1/3    a5 = Ar5 = 27 × 1/243 = 1/9    a6 = Ar6 = 27 × 1/729 = 1/27    ∴ The six GM between 27 and 1/81 are 9, 3, 1, 1/3, 1/9, 1/27

Step-by-step explanation: