In a G.P., the 4^th term is 48 and 7^th term is 384. Find its 6^th term.

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KnowledgeBoat · Accepted Answer

Let first term of G.P. be a and common ratio be r. By formula, ⇒ a_n = ar^{n - 1} Given, 4^th term of G.P. = 48 ⇒ a₄ = 48 ⇒ ar^{4 - 1} = 48 ⇒ ar³ = 48 ..........(1) Given, 7^th term of G.P. = 384 ⇒ a₇ = 48 ⇒ ar^{7 - 1} = 384 ⇒ ar⁶ = 384 ..........(2) Dividing equation (2) by (1), we get : Substituting value of r in equation (1), we get : ⇒ a(2)³ = 48 ⇒ a × 8 = 48 ⇒ a = = 6. ⇒ a₆ = ar^{6 - 1} ⇒ a₆ = ar⁵ ⇒ a₆ = 6 × 2⁵ ⇒ a₆ = 6 × 32 ⇒ a₆ = 192. Hence, 6^th term of G.P. = 192.

Mathematics

In a G.P., the 4^th term is 48 and 7^th term is 384. Find its 6^th term.

AP GP

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Mathematics

In a G.P., the 4th term is 48 and 7th term is 384. Find its 6th term.

AP GP

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Find the 8th term of a G.P., if its common ratio is 2 and 10th term is 768.

In a G.P., the 4^th term is 48 and 7^th term is 384. Find its 6^th term.

Find the 8^th term of a G.P., if its common ratio is 2 and 10^th term is 768.