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integers

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Source: — Problem Solving |
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by pepeprepa » Sat Aug 02, 2008 2:59 pm
I would use a sum formula, that's very common, you can find it in all maths reviews:
"The sum of the k for k=1 to k=n"=(n*(n+1))/2

"The sum of the k for k=1 to k=200"=(200*201)/2
=20100
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by newera » Sat Aug 02, 2008 4:40 pm
another way is:

a) find the number of terms. last number - first number + 1. so 200-0+1=201
b) find the average. add the first and last number and divide by two. so, (200+0)/2=100.
c) multiply. 201*100=20,100
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by sibbineni » Sat Aug 02, 2008 5:10 pm
The terms are in Arithmatic progression

so sum to n terms =n/2(2a+(n-1)d)

n=no of terms
a= first term
d= common difference

here
a=1
n=200
d=1

then sum to 200 terms is==>200/2(2*1+(200-1))
===>100(2+199)
===>100(201)
===>20100

so E
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by malolakrupa » Sat Aug 02, 2008 7:07 pm
sum of first 200 numbers = sum of first 100 numbers + (101+ 102....+ 200)

This equals sum of first 100 numbers + 100* 100 + sum of first 100 numbers

Hence the answer is 2* 5050 + 10000 = 20100
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by eccentric » Sun Aug 03, 2008 10:43 am
I use the formula n + (n(n-1)/2)
the value for 100 is irrelevant just substitute n = 200 in the above formula...
the ans is 20100
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by Scott@TargetTestPrep » Fri Dec 13, 2019 1:02 pm
Nycgrl wrote:The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?
(A) 10,100
(B) 10,200
(C) 15,050
(D) 20,050
(E) 20,100

We can use the formula: average x number = sum. To find the average, we add the first and last numbers and divide by 2. Thus, the sum of the first 200 integers is:

(1 + 200)/2 x 200 = 201 x 100 = 20,100

Alternate solution:

Since the sum of the first 100 positive integers (i.e., 1 to 100) is 5,050 and each of the next 100 positive integers (i.e., 101 to 200) is 100 more than its counterpart in the first 100 integers (101 is 100 more than 1, 102 is 100 more than 2, etc.), then the sum of the integers from 101 to 200 (inclusive) is 100 x 100 = 10,000 more than 5,050, i.e., 15,050. Therefore, the sum of the first 200 positive integers (i.e., 1 to 200) is 5,050 + 15,050 = 20,100.

Answer: E

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