Let be squares such that for each the length of a side of equals the length of a…

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Let

A_1, A_2, A_3, \dots, A_n

be squares such that for each

n \ge 1

the length of a side of

A_n

equals the length of a diagonal of

A_{n+1}

. If the side of

A_1

be 20 units then the smallest value of 'n' for which area of

A_n

is less than 1. (a) 7 (b) 8 (c) 9 (d) 10