Question

Find the average of first 200 positive integers

Answer 1

sum of first n (positive ) no. is n(n+1)/2
= 200*201/2
= 20100
so average is 20100/200
= 100.5

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Answer 2

Hi !

The first positive integers form an A.P ;-

1,2,3, 4 ......

a = 1
 d = 1
n = 200

an = a + (n - 1)d
     = 1 + 199 x 1
     = 200

last term = an = 200

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Sum of first 200 positive integers = Sn

Sn = n/2 [ a + an]
     = 200/2 [ 1 + 200]
     = 100 [ 201]
     = 20100

Average = sum of 200 positive integers/total no: of integers
              = 20100/200
              = 100.5

Average of 200 positive integers = 100.5