Look at the following pattern:
$1^{2} = 1$
$11^{2} = 121$
$111^{2} = 12321$
$1111^{2} = 1234321$
$11111^{2} = 123454321$
Make a conjecture about each of the following:
$111111^{2} =$
$1111111^{2} =$
Check if your conjecture is true.

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Solution

Given pattern $1^{1} = 1$
$(11)^{2} = 121$
$(111)^{2} = 12321$
$(1111)^{2} = 1234321$
$(11111)^{2} = 123454321$
So as per above pattern we get
$(111111)^{2} = 12345654321$
$(1111111)^{2} = 1234567654321$
$∴$ conjecture is true

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Similar questions

Using the pattern 11² = 121 and 111² = 12321, we get 1111² =

1

1 = 11^{o}

2

11 = 11^{1}

3

121 = 11^{2}

4

5

6

n

1111^{2}

1^{2} = 1

11^{2} = 121

111^{2} = 12321

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