Question

What conjecture can you make about the sum of the first 10 odd numbers?

Answer 1

Answer:

The sum 10 first odd numbers are:

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

You can see that the unit part of the numbers repeat, but in the latter 5 numbers we have:

1 + 3 + 5 + 7 + 9 + (10 + 1) + (10 + 3) + (10 + 5) + (10 + 7) + (10 + 9)

Now, we can rearrange this as:

2*(1 + 3 + 5 + 7 + 9) + 5*10

2*(23) + 5*10

now, every number multiplied by a 2, is an even number, and 5*10 = 50 is also an even number.

Here we can see that the sum of the first 10 odd numbers is an even number, and because is an even number different than 2, it is not a prime number.

You can solve the multiplications and get:

2*23 + 5*10 = 46 + 50 = 96

Answer 2

The sum is (10 x 11)/2

(10 x 11)/2=55
1+2+3+4+5+6+7+8+9+10 =55