The 5th term of a g.p. is 1/3 and 9th term is 16/243 find its 4th term

Fifth term , ar4=13   ...1Ninth term ,ar8=16243   ...2Dividing 2 by 1 , we getar8ar4=1624313r4=1681r=±23Substituting the value of r in 1a±234=13a1681=13a=2716Fourth term ,ar3=2716233=12   on taking r = 23Fourth term ,ar3=2716-233=-12   on taking r = -23

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5th trm is 1/3 9th trm is 16/243 a×r raise to the power 4/ a×r raise to the power 8= 81/3×16 = 1/ r raise to the power 4 = 81/16 Or r raise to the power 4 = 16/81 = r= + & - 2/3 And substitute the value of a nd r in formula a×r raise to the power 3 in order to find 4th term.
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