Change set

Pick exam & year, then Go.

Question map
Not attempted Correct Incorrect ★ Bookmarked
Loading…
Q56 (CISF/2024) Miscellaneous & General Knowledge › Important Days, Places & Events

The average of seven consecutive natural numbers is 13. If the next three consecutive natural numbers are also included, the new average will be

Explanation

For any sequence of n consecutive natural numbers, the average is the middle term (if n is odd) or the arithmetic mean of the two middle terms (if n is even). It can also be calculated as (First Term + Last Term) / 2.

Given the average of 7 consecutive numbers is 13, the middle (4th) term is 13. The sequence is: 10, 11, 12, 13, 14, 15, 16.

When the next three consecutive natural numbers (17, 18, and 19) are included, the new sequence becomes: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.

New Average = (First Term + Last Term) / 2 = (10 + 19) / 2 = 29 / 2 = 14.5.

Short Trick: If m subsequent consecutive numbers are added to an existing series of consecutive numbers, the average increases by m/2. Here, m = 3, so the increase is 3/2 = 1.5. New average = 13 + 1.5 = 14.5.

✓ Thank you! We'll review this.

SIMILAR QUESTIONS

CAPF · 2017 · Q109 Relevance score: 4.25

The average of 7 consecutive odd numbers is M. If the next 3 odd numbers are also included, the average

CISF · 2022 · Q48 Relevance score: 0.27

If the sum of five consecutive even numbers is equal to the product of first five natural numbers, then which one of the following is the largest of those even numbers ?

IAS · 2009 · Q67 Relevance score: -0.77

While adding the first few continuous natural numbers, a candidate missed one of the numbers and wrote the answer as 177. What was the number missed ?

CAPF · 2018 · Q34 Relevance score: -1.06

Suppose a, b, c, d and e are five consecutive odd numbers in ascending order. Consider the following statements ; 1. Their average is (a+ 4), 2. Their average is (^ + 2). 3. Their average is te-4). Which of the statements given above is/are correct?