The answer to a problem is: The sequence is $1, 1, 2, 2^0, 2^1$, and the next three terms are $2^0, 2^1, 2^2$, and so on. The first term is $2^0$. Find the smallest positive integer $N$ such that $N > 100$ and the sum of the first $N$ terms of this sequence is an integer power of 2.
A. 440
B. 330
C. 220
D. 110

Let $A _ { 1 } , A _ { 2 } , A _ { 3 } , \ldots$ be squares such that for each $n \geq 1$, the length of the side of $A _ { n }$ equals the length of diagonal of $A _ { n + 1 }$. If the length of $A _ { 1 }$ is 12 cm, then the smallest value of $n$ for which area of $A _ { n }$ is less than one is

Let $A _ { 1 } , A _ { 2 } , A _ { 3 } , \ldots$ be squares such that for each $n \geqslant 1$, the length of the side of $A _ { n }$ equals the length of diagonal of $A _ { n + 1 }$. If the length of $A _ { 1 }$ is 12 cm, then the smallest value of $n$ for which area of $A _ { n }$ is less than one, is