Question

Find the sum without actually adding the following odd numbers:
(1) 1+3+5+ 7 + ... ... ... +35
​

Answer 1

The sum of any set of consecutive odd numbers starting with 1 is always equal to the square of the number of digits that were added together.

18*18

=324

Answer 2

Sum of 1 + 3 + 5 + 7 + ........ + 35 is 324

Solution:

Given that, we have to find the sum

Given is:

1 + 3 + 5 + 7 + ........ + 35

The sum of n odd numbers is given as:

The sum of any set of consecutive odd numbers starting with 1 is always equal to the square of the number of digits that were added together

Therefore,

$Sum = n^2$

Here, total odd numbers from 1 to 35 is 18

$Sum = 18^2\\\\Sum = 18 \times 18\\\\Sum = 324$

Thus sum is 324

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