Without addition find: $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + . . . . + 33$

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Solution

Sum of first $n$ consecutive odd numbers is $n^{2}$
Here, $n = 17$
Therefore
$1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + . . . + 33 = (17)^{2} = 289$

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Similar questions

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

1 + 3 + 5 + 7 + 9

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

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

1 + 3 + 5 + 7 + 9

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

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

Without adding find the sum

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

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

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

Question 7 (iii)
Without adding, find the sum:

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

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