Question

1. The sum of first in odd natural numbers is 196. The value of 'n' is,​

Answer 1

Answer:

14

Step-by-step explanation:

it is a statement of squares saying that THE SUM OF FIRST N ODD NATURAL NUMBER IS EQUAL TO N^2 SO 14 ^2 IS 96

Answer 2

The value of 'n' is 14.

Solution:

The first number of the odd series is 1 and the second number is 3.

So the common difference d = (3-1) = 2

So here, a = 1, d = 2 and the sum S = 196

Hence,

$S=\frac{n \times(2 a+(n-1) \times d)}{2}$

$\Rightarrow 196=\frac{n \times(2 \times 1+(n-1) \times 2)}{2}$

$\Rightarrow 196=\frac{n \times(2+2 n-2)}{2}$

$\Rightarrow \quad 196=\frac{n \times(2+2 n-2)}{2}$

$196=\frac{n \times 2 n}{2}$

$\Rightarrow 196=n^{2}$

$\Rightarrow n=14$

So, the value of n = 14.