(a) The given sequence is, 2,2√2,4,...
Clearly given sequence is in G.P
With a=2 and r=2√22=√2
Let the nth term of the given sequence be 128.
an=arn−1⇒(2)(√2)n−1=128⇒(2)(2)n−12=(2)7⇒(2)n−12+1=(2)7⇒n−12=6⇒n−1=12⇒n=13
Thus, the 13th term of the given sequence is 128.
(b) The given sequence is √3,3,3√3
Clearly this sequence is in G.P
with, a=√3 and r=3√3=√3
Let the nth term of the given sequence be 729.
an=arn−1⇒arn−1=729⇒(√3)(√3)n−1=729⇒(3)12(3)n−12=(3)6∴12+n−12=6⇒1+n−12=6⇒n=12
Thus, the 12th term of the given sequence is 729.
(c) The given sequence is, 13,19,127,...
Clearly this sequence is in G.P
With a=13 and r=19÷13=13
Let the nth term of the given sequence be119683
an=arn−1⇒arn−1=119683⇒(13)(13)n−1=119683⇒(13)n=(13)9⇒n=9
Thus, the 9th term of the given sequence is 119683