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The Product of 3rd and 8th Terms of a G.P. is 243. If Its 4th Term is 3, Find Its 7th Term. - Mathematics

Sum

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

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Solution

Let the first term of the G.P. be a and its common ratio be r.
Now,
t3 x t8 = 243
⇒ ar2 x ar7 = 243
⇒ a2r9 = 243   ....(i)
Also,
t4 = 3
⇒ ar3 = 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`

⇒ r3 = 27
⇒ r = 3

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

∴ 7th term = t7 = ar6 = `1/9` x (3)6 = 81

Concept: Simple Applications - Geometric Progression
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APPEARS IN

Selina Concise Maths Class 10 ICSE
Chapter 11 Geometric Progression
Exercise 11 (B) | Q 5 | Page 154
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