CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

Let S1,S2 be squares such that for each n1, 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 less than 1 sq. cm?

A
7
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
8
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
9
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
10
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 10
(b), (c), (d)
If a be the side of a square, then d=a2
By given condition an=2an+1
or an+1=an2=an1(2)2=an2(2)3=a1(2)n
Replacing n by n-1, we get
an=a1(2)n1=102n1/2
Area of Sn<1a2n<1
1002n1<1 or 200<2n or 2n>200
Now 27=128<200<28=256>200
n=8,9,10(b), (c), (d)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon