Find the geometric progression whose 4th term is 54 and the 7th term is 1458.

Question

KnowledgeBoat · Accepted Answer

Given, a₄ = 54 and a₇ = 1458. By formula, a_n = ar^{n - 1}. ⇒ a₄ = a(r)^{4 - 1} ⇒ 54 = ar³ (Eq 1) ⇒ a₇ = a(r)^{7 - 1} ⇒ 1458 = a(r)⁶ (Eq 2) Dividing Eq 2 by Eq 1, Putting value of r in Eq 1, a₂ = ar = 2 × 3 = 6 a₃ = ar² = 2(3)² = 2 × 9 = 18 a₄ = ar³ = 2(3)³ = 2 × 27 = 54. Hence, the required G.P. is 2, 6, 18, 54, ...

Mathematics

Find the geometric progression whose 4th term is 54 and the 7th term is 1458.

AP GP

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Mathematics

Find the geometric progression whose 4th term is 54 and the 7th term is 1458.

AP GP

Related Questions

The 5th, 8th and 11th terms of a G.P. are p, q and s respectively. Show that q2 = ps.

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Three numbers are in A.P. and their sum is 15. If 1, 4 and 19 are added to these numbers respectively, the resulting numbers are in G.P. Find the numbers.

The 5th, 8th and 11th terms of a G.P. are p, q and s respectively. Show that q² = ps.

If a, a² + 2 and a³ + 10 are in G.P., then find the value(s) of a.