sum

I don't want to say that you should necessarily do it this way, but 1+3+5+7+9+11+13+15+17+19+21+23=144 so 12

Notice a pattern on the partial sums:

1 = 1 = 1^2

1 + 3  = 4 = 2^2

1 + 3 + 5 = 9 = 3^2

1 + 3 + 5 + 7 = 16 = 4^2

The sum is equal to n^2, where n is the number of terms. (This can be proven by mathematical induction.)

Now, 144 = 12^2. This means n^2 = 12^2, n = 12.

this is a perfect square pattern. so all we need to find is sqrt144=12 so n=12