Sum

The product of 3^{rd} and 8^{th} terms of a G.P. is 243. If its 4^{th} term is 3, find its 7^{th} term.

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#### Solution

Let the first term of the G.P. be a and its common ratio be r.

Now,

t_{3} x t_{8} = 243

⇒ ar^{2} x ar^{7} = 243

⇒ a^{2}r^{9} = 243 ....(i)

Also,

t_{4} = 3

⇒ ar^{3} = 3

⇒ a =`3/"r"^3`

Substituting the value of a in (i), we gwt

`(3/"r"^3)^2xx"r"^9=243`

`=> 9/r^6xxr^9=243`

⇒ r^{3} = 27

⇒ r = 3

`=>a=3/3^3=3/27=1/9`

∴ 7^{th} term = t_{7} = ar^{6} = `1/9` x (3)^{6} = 81

Concept: Simple Applications - Geometric Progression

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