. Without adding find the sum


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

(ii) 1+3+5+7+9+11+13++1517+19

(iii) 1+3+5+7+9+11+13++1517+19+21+23

Best Answer

Explanation:

(i) 1+3+5+7+9

We can observe that 1,3,5,7,9 are 5 consecutive odd numbers.

Therefore, n = 5

The sum of consecutive odd number = n2

Put n=5

We get,

⇒5×5

⇒25

(ii) 1+3+5+7+9+11+13++1517+19

We can observe that 1,3,5,7,9,11,13,15,17,19 are 10 consecutive odd numbers.

Therefore, n = 10

The sum of consecutive odd number = n2

Put n=10

We get,

⇒10×10

⇒100

(iii) 1+3+5+7+9+11+13++1517+19+21+23

We can observe that 1,3,5,7,9,11,13,15,17,19,21,23 are 12 consecutive odd numbers.

Therefore, n = 12

The sum of consecutive odd number = 

Put n=12

We get,

⇒12×12

⇒144

Final Answer:

(i) 1+3+5+7+9= 25

(ii) 1+3+5+7+9+11+13++1517+19= 100

(iii)  1+3+5+7+9+11+13++1517+19+21+23= 144

 

 

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