Find the average of all odd numbers up to 100 (1) 30 (2) 50 (3) 4 (4) 10

Answer: (2)

Odd numbers are defined as any number which cannot be divided by two. In other words, a number of form 2k+1, where k ∈ Z (i.e. integers) are called odd numbers.

There are 50 odd numbers from 1 to 100.

From 1 to 100 sum of the odd numbers are = 1+3+5+7+9+….+93+95+97+99

We can solve the question by Arithmetic Progression(AP) formula

Let us consider

a = 1

l = 99

d = 2

T(n) = a + (n – 1)d

99 = 1 + (n – 1)2

98 = 2n – 2

100 = 2n

n = 50

Now consider

S(n) = n/2(a + l)

S(50) = 50/2 (1 + 99)

S(50) = 2500

Avaregae sum = Sum of numbers / Total number

Avaregae sum = 2500/50

Avaregae sum = 50.

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