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Ex.6.1 Q7 Squares and Square Roots Solutions - NCERT Maths Class 8

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Question

Without adding, find the sum.

(i)

\(1 + 3 + 5 + 7 + 9\)

(ii)

\(\left[ \begin{align} &1  + 3  +  5  +  7  +  9  +  11  +  \\ &13  +  15  +  17  +  19 \\  \end{align} \right]\)

(iii)

\(\left[ \begin{align} &1  +  3  +   5  +  7  +  9  +  11  +  13  +  \\  &15  +  17  +  19  +  21  +  23 \\  \end{align} \right]\)

 Video Solution
Squares And Square Roots
Ex 6.1 | Question 7

Text Solution

What is known?

Consecutive odd numbers.

What is uknown?

Sum of these consecutive odd number without adding.

Reasoning:

Sum of the first n odd natural numbers is \(n^2\) .

Steps:

(i) \(1 + 3 + 5 + 7 + 9\)

Here number of term \((n)\) is \(5\)

\({\mathop{\rm Sum}\nolimits} = {(5)^2} = 25\)

(ii)

\(\left[ \begin{align} &1  + 3  +  5  +  7  +  9  +  11  +  \\ &13  +  15  +  17  +  19 \\  \end{align} \right]\)

Here number of term \((n) \) is \(10\)

\({\mathop{\rm Sum}\nolimits} = {(10)^2} = 100\)

(iii)

\(\left[ \begin{align} &1 + 3 +  5 + 7 + 9 + 11 + 13 + \\ &15 + 17 + 19 + 21 + 23 \\ \end{align} \right]\)

Here number of term \( (n)\) is \(12\)

\({\mathop{\rm Sum}\nolimits} = {(12)^2} = 144\)