Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit

Question

TOUGH QUESTION:

Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit squares, respectively. If the pattern were continued, how many nonoverlapping unit squares would there be in figure 100?

(A) 10401
(B) 19801
(C) 20201
(D) 39801
(E) 40801

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Official Answer

C

Samine · Answer

Here is my solution:

From figure 0 to figure 100, we have 101 figures
The given sequence here is: 1, 5, 13, 25,.... the next number will be 41
=> new sequence (which is the difference between 2 numbers) is 4, 8, 12, 16,... This is an evenly spaced set, so the last number of this sequence is = 4 + (100-1)*4 = 400
This new sequence have average = (last number + first number) / 2 = (400 + 4) / 2 = 202
Because this is an evenly spaced set,  Sum = average * total number of sequence = 202 * 100 = 20200

Notice the pattern here: 
5 = 1+4
13 = 1+4+8
25 = 1+4+8+12
....
x (figure 100) = 1 + 20200 = 20201 => Option C

Correct me if I'm wrong!

Shobhit7 · Answer

Pattern formulae: first term + 2

For figure no 100 and first term 1, no of squares: 1+2(100*101) = 1 + 2(10100) = 1+20200 = 20201

Ans C

Mani2879 · Answer

There is pattern here:
Figure ........................................ No of unit squares 
0 -------------------> 1------------------------> 1 square-----> 1
1 ------------------->1,3,1--------------------->5-------------> 2 square + 1 square
2 ------------------->1,3,5,3,1----------------->13------------>3 sq + 2 sq
3 ------------------->1,3,5,7,5,3,1------------->25------------>4 sq + 3 sq
;
;
;
;
Similarly,
100--------------------------------------------------------------->101 sq + 100 sq = 10201 + 10000 = 20201

teja18892 · Answer

Why can't this be the answer?

N=1, SQ=1
N=2, SQ=5 
N=3, SQ=13 ((3*3)+(2*2))= 13
N=4, SQ=25 ((N*N) + (N-1)^2) , For eg ((4*4) + (3*3)) = 25

So For N-100

((100*100) + (99*99)) = 19,801

AbhishekB19 · Answer

Well I had a different take on this -

Fig 1 - 5Sq ----> 1*(2+2)+1 = 5
Fig 2 - 13Sq ---> 2*(4+2)+1 = 13
Fig 3 - 25Sq ---> 3*(6+2)+1 = 25
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Fig 100 ----> 100 * (200+2)+1 = 20201

AbhishekB19 · Answer

---------------------
Because you have mistakenly quoted fig 0 as fig 1. The correct sequence will be : SQ(n)= {(N+1)^2} + (N^2).
For SQ(n) = 100
  = 10201 + 10000 = 20201

Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit

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Figures 0, 1, 2, and 3 consist of 1, 5, 13, and 25 nonoverlapping unit

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