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)

$2,2^2,2^4,2^8,2^{16}\dots \dots$.
Consider the exponents on 2 's, we have $1,2,2^2,2^3,2^4,\dots \dots$.
Hence power on the $10^{\text{th }}$ term is $2^9=512$ (i.e. $t_{10}=2^{2^9}$ ) $T_{10}=2^{512}=(16{)}^{128}>10^{100}$