Without adding, find the sum: (i) (1 + 3 + 5 + 7 + 9 + 11 + 13) (ii)

1.	Without adding, find the sum: (i) (1 + 3 + 5 + 7 + 9 + 11 + 13) (ii) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19) (iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23)
Answer» (i) We know that, Sum of first n odd numbers = n² Applying this formula in the question, we get (1 + 3 + 5 + 7 + 9 + 11 + 13) = (7)² = 49 (ii) We know that, Sum of first n odd numbers = n² Applying this formula in the question, we get (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19) = (10)² = 100 (iii) We know that, Sum of first n odd numbers = n² Applying this formula in the question, we get (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23) = (12)² = 144

Without adding, find the sum: (i) (1 + 3 + 5 + 7 + 9 + 11 + 13) (ii) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19) (iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23)

Answer»

(i) We know that,

Sum of first n odd numbers = n²

Applying this formula in the question, we get

(1 + 3 + 5 + 7 + 9 + 11 + 13) = (7)²

= 49

(ii) We know that, Sum of first n odd numbers = n²

Applying this formula in the question, we get

(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19) = (10)²

= 100

(iii) We know that,

Sum of first n odd numbers = n²

Applying this formula in the question, we get

(1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23)

= (12)²

= 144