Question

√3,3,3√3...........is 729?

Answer 1

The given sequence is 3–√,3,33–√.........3,3,33.........

This sequence is a G.P.since the ratio of any two successive terms is same.

1stterm1stterm of the G.P.=a=3–√=a=3 and common ratio=r=33–√=r=33=3–√=3

We know that tn=a.rn−1tn=a.rn−1

Also given that tn=729tn=729

⇒729=a.rn−1=3–√.(3–√)n−1=(3–√)n−1+1=(3–√)n⇒729=a.rn−1=3.(3)n−1=(3)n−1+1=(3)n

729=36729=36 and 3–√=31/23=31/2

⇒36=3n/2⇒36=3n/2

Since the base on either side is equal (=3) the powe on either side is also equal.

⇒6=n2⇒6=n2 or n=12n=12

i.e.,12thi.e.,12th term of the given sequence is 729