Question

The first term of a geometric progression is 12 and the fifth term is 55. Determine the 11th term.​

Answer 1

Answer:

12 (55/12)^(5/2)   or  55^(5/2) / 12^(3/2)   or  539.68

Step-by-step explanation:

nth term of GP = arⁿ⁻¹.  In the given question,

    first term of GP = 12

               ∴ a = 12             ...(1)

    fifth term of GP = 55

             ∴ ar⁴ = 55           ...(2)

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

  ⇒ ar⁴/a = 55/12

  ⇒ r⁴ = 55/12

  ⇒ r = (55/12)^(1/4)

Hence,

⇒ 11th term  =  ar¹⁰

                    = (12) ((55/12)^(1/4) )¹⁰

                    = 12 (55/12)^(5/2)

Or solving further, we get 11th term ≈ 539.68

Answer 2

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• Refer the attachment!! ;)