Question 12

Write the correct answer from the given four options.

The sum of first n odd natural numbers is

a) $2 n + 1$
b) $n^{2}$
c) $n^{2} - 1$
d) $n^{2} + 1$

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Solution

Sum of first n odd natural numbers $= \sum (2 n - 1) = 2 \sum n - n$
$= \frac{2 \times n (n + 1)}{2} - n = n (n + 1) - n = n^{2} + n - n = n^{2}$

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$1 + 3 + 5 + . . . . . + (2 n - 1) = n^{2}$ i.e., the sum of first n odd natural numbers is $n^{2}$ .

\frac{n + 1}{2}

\frac{n}{2}

1^{2} + {2.2}^{2} + 3^{2} + {2.4}^{2} + 5^{2} + {2.6}^{2} + \dots . i s \frac{n}{2} (n + 1)^{2}

Question 11

Write the correct answer from the given four options.

The sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15 is

a) 81
b) 64
c) 49
d) 36

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