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Given series is 2,22–√,4,.........2,22,4,.........
This series is G.P. since the ratio of any two successive terms is same.
first term=a=2=a=2 and common ratio r=22–√2r=222=2–√=2
We know that nth term =tn=a.rn−1=tn=a.rn−1
Given that tn=128tn=128
⇒128=2.(2–√)n−1⇒128=2.(2)n−1
2–√=21/22=21/2 and 128=27128=27
⇒27=2(1+n−12)⇒27=2(1+n−12)
Since the base on either side is 2, power on both sides are equal.
⇒7=1+n−12=n+12⇒7=1+n−12=n+12
or n=13n=13
i.e.,13thi.e.,13th term of the sequence is 128
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