Find 5 geometric means between 1 and 27.

Question

KnowledgeBoat · Accepted Answer

Let a, b, c and d be the 5 geometric means 1 and 27. ∴ 1, a, b, c, d, e and 27 are in G.P. So, first term (a) = 1 and seventh term = 27. Let common ratio be r. ∴ ar⁶ = 27 ⇒ (1)r⁶ = 27 ⇒ r⁶ = 3³ ⇒ r⁶ = ⇒ r = . Second term = ar = , Third term = ar² = , Fourth term = ar³ = , Fifth term = ar⁴ = , Sixth term = ar⁵ = . Hence, 5 geometric means between 1 and 27 = .

Mathematics

Find 5 geometric means between 1 and 27.

AP GP

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Mathematics

Find 5 geometric means between 1 and 27.

AP GP

Related Questions

If the sum of first m terms of an A.P. is n and sum of first n terms of the same A.P. is m, show that sum of first (m + n) terms of it is -(m + n).

3rd term of a G.P. is 27 and its 6th term is 729; find the product of its first and 7th terms.

Find the sum of the sequence 96 - 48 + 24 ……… upto 10 terms.

Find the sum of first n terms of :(i) 4 + 44 + 444 + ……(ii) 0.7 + 0.77 + 0.777 + …….

3^rd term of a G.P. is 27 and its 6^th term is 729; find the product of its first and 7^th terms.

Find the sum of first n terms of :
(i) 4 + 44 + 444 + ……
(ii) 0.7 + 0.77 + 0.777 + …….