Question

14. How much greater is the sum of the first 50 counting numbers greater than the sum of the first 100 counting numbers? a. 110 b. 3,775 c. 3,155 d. 1200

Answer 1

Answer:

b. 3.775

Step-by-step explanation:

The question is worded incorrectly since the sum of the first 100 counting numbers is actually greater than the sum of the first 50 counting numbers.

The sum of any set of consecutive numbers of size 'n' is given by:

$S = \frac{(A_1+A_n)*n}{2}$

Where A1 is the first number on the set and An is the last number.

The sum of the first 100 counting numbers (1 through 100) is:

$S_{100}= \frac{(1+100)*100}{2}=5,050$

The sum of the first 50 counting numbers (1 through 50) is:

$S_{50}= \frac{(1+50)*50}{2}=1,275$

The difference between those two values is:

$S_{100} -S_{50} =5,050-1,275=3,775$

Therefore, the sum of the first 100 counting numbers is 3,775 greater than the sum of the first 50 counting numbers.