Question

1. Express $49$ as the sum of $7$ odd numbers.
2. Express $121$ as the sum of $11$ odd numbers.

Answer 1

We know that the sum of first $n$ odd natural numbers is $n^2$.
(i) $49 = (7)^2$
Therefore, $49$ is the sum of first $7$ odd natural numbers.
$49 = 1 + 3 + 5 + 7 + 9 + 11 + 13$

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(ii) $121 = (11)^2$
Therefore, $121$ is the sum of first $11$ odd natural numbers.
$121 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21$