Question

Find the average of all the odd numbers between 60 to 100.

1. 60
2. 80
3. 160
4. 100

Answer 1

Correct Answer - Option 2 : 80

Given:

Range of numbers from 60 to 100 is given.

Formula Used:

S_n = (n/2) × (a + l)

where, n = Number of terms in A.P.

a = First term of the A.P.

l = Last term of the A.P.

Calculation:

According to the question,

The odd numbers between 60 to 100 are,

61, 63, 65,...….., 95, 97 and 99.

Here, The odd numbers are in A.P.

So, the first term, a = 61

& last term, l = 99

& common difference, d = 63 - 61

⇒ 2

& number of terms, n = (100 – 60)/2

⇒ 40/2

⇒ 20

So, Sum of all the terms of this AP = (n/2) × (a + l)

⇒ 10 × (61 + 99)

⇒ 10 × 160

⇒ 1600

Now, The average of all the odd numbers = (Sum of all the odd numbers between 60 to 100)/(Number of odd numbers between 60 to 100)

⇒ 1600/20

⇒ 80

∴ The average of all the odd numbers between 60 to 100 is 80.