SOLUTION: Find the sum of the first 50 even positive integers. Select one: a. 2,550 b. 2,650 c. 2,600 d. 2,500

Question 1194645: Find the sum of the first 50 even positive integers.
Select one:
a.
2,550

b.
2,650

c.
2,600

d.
2,500
Found 2 solutions by math_tutor2020, Alan3354:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

A = Set of first 50 positive even integers
A = {2, 4, 6, ..., 98, 100}
A = {2*1, 2*2, 2*3, ..., 2*49, 2*50}

Adding those items gets us this expression:
2*1+2*2+2*3+...+2*49+2*50
2*(1+2+3+...+49+50)

From here we need to calculate the sum of the first 50 positive integers

S = sum of the first n positive integers
S = n*(n+1)/2
S = 50*(50+1)/2
S = 50*51/2
S = 25*51
S = 1275
which point us to
1+2+3+...+49+50 = 1275

Therefore,
2*(1+2+3+...+49+50) = 2*1275 = 2,550

Answer: Choice A) 2,550

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find the sum of the first 50 even positive integers.
-----------
Make 25 pairs:
2 + 100
4 + 98
6 + 96
etc
---> 102*25 = 2550
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