The sum of the first 50 positive integers is 1, 275. What is the sum

Question

The sum of the first 50 positive integers is 1, 275. What is the sum of the integers from 51 to 100.

(A) 2, 525
(B) 2, 550
(C) 3, 250
(D) 3, 775
(E) 5, 050

fall2021 · Accepted Answer

From 51 to 100 each number is 50 higher than corresponding numbers in 1 to 50.

So the increase in total will be 50*50 = 2500

Total sum = 1275 + 2500 = 3775

Option D

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akadiyan · Answer

Sum of consecutive integers =  \frac{(First+Last)}{2}  * Number of integers

First digit = 51
Last digit = 100

Sum of consecutive integers from 51 to 100 =  \frac{51+100}{2}  * 50 = 3775

Ans   D

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • The sum of the first 50 positive integers is 1,275

To find  
We need to determine
 • The sum of the integers from 51 to 100

Approach and Working out

• 1 + 2 + 3 + … + 50 = 1,275 (given)
• 51 + 52 + 53 + … + 100
 o = (50 + 1) + (50 + 2) + (50 + 3) + … + (50 + 50)
o = (50 + 50 + 50 + … + 50) + (1 + 2 + 3 + … + 50) 
o = (50 × 50) + 1,275
o = 2,500 + 1,275
o = 3,775

Thus, option D is the correct answer.

Correct Answer: Option D

Pritishd · Answer

Method-I (Using the formula to find the sum of first n positive integers)  
1. We are give the sum of the first  50  positive integers i.e.  1275 
2. Therefore, the SUM(51 to 100) = SUM(1 to 100) - SUM(1 to 50)
3. SUM(1 to 100)  =   \frac{n(n + 1)}{2}  where  n = 100 . Solving, we get,  \frac{100*101}{2}   =   3775 
4. SUM(51 to 100)  = 5050 - 1275 = 3775

Method-II (Using the mean formula)  
1. Mean = Sum of all the elements in a set / Total number of elements
2. Rearranging, we get Sum of all the elements in a set = Mean * Total number of elements
3. In our case, Mean = First element + Last element/2  = \frac{51 + 100}{2} = \frac{151}{2} 
4. Total number of elements = Last element - First element + 1  = 100 - 51 + 1 = 50 
5. Putting 3. and 4. together we get,  \frac{151}{2} * 50 = 3775

Ans.  D

ScottTargetTestPrep · Answer

Solution:
 
51 + 52 + 53 + … + 100

= (1 + 50) + (2 + 50) + (3 + 50) + … + (50 + 50)

= (1 + 2 + 3 + … + 50) + … + (50 + 50 + 50 + … + 50)

= 1,275 + 50 x 50

= 1,275 + 2,500

= 3,775

Answer: D

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The sum of the first 50 positive integers is 1, 275. What is the sum

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The sum of the first 50 positive integers is 1, 275. What is the sum

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