the arithmetic mean of first natural numbers

Question

(a) n+1/2

(b)n-1/2

(c)n/2

(d)n

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Answer 1

find the arithmetic mean of the first "n" natural numbers

look at the pattern:

(1+2)/2=3/2=1.5 and the next natural number is 3 and 3/2=1.5

(1+2+3)/3=6/3=2 and the next natural number is 4 and 4/2=2

(1+2+3+4)/4=10/4=2.5 and the next natural number is 5 and 5/2=2.5

(1+2+3+4+...+n-1+n)/n=(n+1)/2 which is (a)