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Observe the following pattern and supply the missing numbers. 11^2 = 121 101^2 = 10201 10101^2 = 102030201 1010101^2 = ........................... ............2 = 10203040504030201

Observe the following pattern and supply the missing numbers. 11^2 = 121
101^2 = 10201
10101^2 = 102030201
1010101^2 = ...........................
............2 = 10203040504030201 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
8 months ago
Dear Student

We observe that the square on the number on R.H.S of the equality has an odd number of digits such that the first and last digits both are 1. And, the square is symmetric about the middle digit. If the middle digit is 4, then the number to be squared is 10101 and its square is 102030201.
So, 1010101^2=1020304030201
101010101^2=10203040505030201

Thanks

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