Let A 1 , A 2 , A 3 , … . . be squares such that for each n ⩾ 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

Question

Let A 1 , A 2 , A 3 , &#8230; . . be squares such that for each n &#10878; 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 &#160; cm , then the smallest value of n for which area of A n is less than one, is

Aicharya · Accepted Answer

Let a n be the side length of A n . So, a n = 2 a n + 1 , a 1 = 12 &#8658; &#160; a n = 12 &#215; 1 2 n - 1 Now, a n 2 &#60; 1 &#8658; 144 2 n - 1 &#60; 1 &#8658; &#160; 2 n - 1 &#62; 144 &#8658; &#160; n - 1 &#8805; 8 &#8658; &#160; n &#8805; 9

Let A 1 , A 2 , A 3 , … . . be squares such that for each n ⩾ 1 , the length of the side of A n…

Solution

Let A 1 , A 2 , A 3 , &#8230; . . be squares such that for each n &#10878; 1 , the length of the side of A n…

Solution

Let A 1 , A 2 , A 3 , … . . be squares such that for each n ⩾ 1 , the length of the side of A n…