3. What conjecture can you make about the sum of the first 10 integers?

Question

3. What conjecture can you make about the sum of the first 10 integers?

1                                 = 1 = (1x2)/2

1+2                             = 3 = (2x3)/2

1+2+3                         = 6 = (3x4)/2

1+2+3+4                     = 10 =(4x5)/2

1+2+3+4+5                 = 15 = (5x6)/2

 

(1 point)

 

A.The sum is (9 x 10)/2

 

B.The sum is (9 · 10)

 

C.The sum is (10 x 11)/2

 

D.The sum is (10 · 11)

Answer 1

When the maximum number is N, the sum=(N+(N+1))/2

 

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

 

So the answer is C.

 

The more formal way is like this:

Consider 1+2+3

Assume S=1+2+3

 

S=1+2+3

S=3+2+1

 

Adding these 2 equations 

2S= (1+3)+(2+2)+(3+1) 

This equation has 3 pairs with each pairs equal to 4

 

2S= 4*3

S=4*3/2

In this equation, 4=1+max number (which is 3), 3 is the total number in S