Question

The average of 10 concecutive odd numbers is 120. what is the average of the smallest number among them


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Answer 1

Answer:

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Answer 2

• Let us assume, 2n – 9, 2n – 7, 2n – 5, 2n – 3, 2n – 1, 2n + 1, 2n + 3, 2n + 5, 2n + 7, 2n + 9 are the 10 consecutive odd numbers for any positive integer n.

Given:

⇒(2n – 9 + 2n – 7 + 2n – 5 + 2n – 3 + 2n – 1 + 2n + 1 + 2n + 3 + 2n + 5 + 2n + 7 + 2n + 9) / 10 = 120

⇒20n / 10 = 120

⇒2n = 120

⇒n = 60

• Hence, 2n – 9 = 120 – 9 = 111. This is first odd number

• Therefore, the 10 consecutive odd numbers are 111, 113, 115, 117, 119, 121, 123, 125, 127, 129

• Therefore, the average of the smallest five odd numbers in the above series is 115.

⇒Average = (111 + 113 + 115 + 117 + 119) / 5

⇒ 575 / 5 = 115.