Question

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

Answer 1

Step-by-step explanation:

1. 1+3+5+7

= total no. is 4 = square of 4

= 16 is the answer.

2. 1+3+5+7+9+11+13

= total no. is 7= square of 7

49 is the answer.

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

= total number is 12 = square of 12

= 144 is the answer.

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Answer 2

Step-by-step explanation:

1) 1 + 3 + 5 + 7 + 9

Total consecutive odd numbers = 5

Thus, n = 5

Therefore, sum = n2

= 5 × 5 = 25

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

Total consecutive odd numbers = 10

Thus n = 10

Therefore sum = n × n

= 10× 10 = 100

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

Total consecutive odd numbers = 12

Thus n = 12

Therefore sum = n × n

= 12× 12 = 144

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