Find the G.P. whose 5th and 8th terms are 80 and 640 respectively.

Question

KnowledgeBoat · Accepted Answer

Let a be the first term and r be the common ratio. We know that, nth term of a G.P. is given by, Tn = arn - 1 Given, 5th term = 80 ⇒ ar5 - 1 = 80 ⇒ ar4 = 80 ....(1) Given, 8th term = 640 ⇒ ar8 - 1 = 640 ⇒ ar7 = 640 .......(2) Dividing Equation (2) by Equation (1) : Substituting r = 2 in Equation (1), we get : ⇒ a(2)4 = 80 ⇒ 16a = 80 ⇒ a = ⇒ a = 5. G.P. is, 5, 5(2), 5(2)2, 5(2)3..... 5, 10, 20, 40, ..... Hence, the G.P. is 5, 10, 20, 40, ......

Mathematics

Find the G.P. whose 5th and 8th terms are 80 and 640 respectively.

G.P.

Related Questions

Which term of the G.P. 5, 10, 20, 40,…… is 640?

The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series.