Question

With out addition find the sum 1+3+5+7+9+11+13+15+17+19+21+22+ 23

Answer 1

Hi there

Your answer is :-

( Note :- Make it an AP we have to remove 22 . Then only it can be add without performing actual addition .)

a = 1

d = 2

n = ?


a + ( n - 1 ) d = 23

1 + ( n - 1 ) 2 = 23

( n - 1 ) 2 = 23 - 1

n - 1 = 22/2

n = 11 + 1

n = 12


Now the sum of the numbers ( Sn ) :-

Sn = n [ 2a + ( n - 1 ) d ] / 2

Sn = 12 (2 ( 1 ) + ( 12 - 1 ) 2 ) / 2

Sn = 12 ( 2 + 11 ( 2 ) ) / 2

Sn = 12 ( 2 + 22 ) / 2

Sn = 12 ( 24 ) / 2

Sn = 288 / 2

Sn = 144 ( Ans )

Answer 2

Hello!!
Here is your answer.

I think u mistakenly added 22 in the question.

So, Correct Question 》
1+3+5+7+9+11+13+15+17+19+21+23.

Sum of n consecutive odd numbers = n^2.

Here, we have to find sum of 12 consecutive odd numbers. So,
1+3+5+7+9+11+13+15+17+19+21+22+ 23 = 12×12 = 144.

Hope It Helps