Question

Given a sequence of ten numbers, if the first number is 2 and each other number is the square of the preceding number, then the tenth number is

• A. between 10 and $10^5$
• B. between $10^5$ and $10^{10}$
• C. between $10^{50}$ and $10^{100}$
• D. more than $10^{100}$

Answer 1

Answer: (D)

$ 2,2^2, 2^4, 2^8, 2^{16} \ldots \ldots$.
Consider the exponents on 2 's, we have $1,2,2^2, 2^3, 2^4, \ldots \ldots$.
Hence power on the $10^{\text {th }}$ term is $2^9=512 $ (i.e. $t _{10}=2^{2^9}$ ) $T _{10}=2^{512}=(16)^{128}>10^{100}$