Question
Let S1, S2,....... be squares such that for each n≥1, the length
of a side of Sn equals the length of a diagonal of Sn+1. If the
length of a side of S1 is 10 cm, then for which of the following
values of n is the area of Sn greater then 1sq cm
of a side of Sn equals the length of a diagonal of Sn+1. If the
length of a side of S1 is 10 cm, then for which of the following
values of n is the area of Sn greater then 1sq cm
Answer: Option A
:
A
(b, c, d) Given xn = xn+1 √2
∴x1 =x2√2,x2 =x3√2,xn =xn+1√2
On multiplyingx1 =xn+1 (√2)n ⇒xn+1 = x1(√2)n
Hencexn = x1(√2)n−1
Area ofSn = x2n = x2n2n−1 < 1 ⇒ 2n−1 >x21 (x1 = 10)
∴2n−1 > 100
But27 > 100,28>100, etc.
∴ n - 1 = 7, 8, 9....... ⇒ n = 8, 9, 10.........
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:
A
(b, c, d) Given xn = xn+1 √2
∴x1 =x2√2,x2 =x3√2,xn =xn+1√2
On multiplyingx1 =xn+1 (√2)n ⇒xn+1 = x1(√2)n
Hencexn = x1(√2)n−1
Area ofSn = x2n = x2n2n−1 < 1 ⇒ 2n−1 >x21 (x1 = 10)
∴2n−1 > 100
But27 > 100,28>100, etc.
∴ n - 1 = 7, 8, 9....... ⇒ n = 8, 9, 10.........
Was this answer helpful ?
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