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

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)
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1 Answer

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