Average and Middle Number (Odd Number of Terms)
If you have an odd number of terms (like 3, 5, or 7), the average of the series is always the exact middle number.
Average and Middle Number (Even Number of Terms)
- If you have an even number of terms (like 4, 6, or 8), the average is not a number in the series.
- Instead, the average is the number that falls exactly between the two middle numbers.
Common Difference (CD)
- For consecutive even numbers, the common difference is 2 (example, 4, 6, 8).
- For consecutive odd numbers, the common difference is also 2 (example, 3, 5, 7).
- For consecutive integers, the common difference is 1 (example, 5, 6, 7).
Practice Questions and Answers
1. The sum of 6 consecutive even numbers is 270. What is the highest number in the series?
Correct Answer: 50
Rationale: The average of the 6 consecutive even numbers is 270 / 6 = 45. The numbers are 40, 42, 44, 46, 48, 50. The highest number is 50.
2. The average of 5 consecutive odd numbers is 63. What is the lowest number in the series?
Correct Answer: 59
Rationale: Since there are 5 consecutive odd numbers, the average (63) is the middle number. The series is 59, 61, 63, 65, 67. The lowest number is 59.
3. The sum of three consecutive numbers is 18. What are the three numbers?
Correct Answer: 5, 6, 7
Rationale: The average of the numbers is 18 / 3 = 6. This is the middle number. The three consecutive numbers are 5, 6, 7.
4. If the sum of 4 consecutive even numbers is 108, what is the third number in the series?
Correct Answer: 28
Rationale: The average of the numbers is 108 / 4 = 27. The four consecutive even numbers are 24, 26, 28, 30. The third number is 28.
5. The sum of 5 consecutive numbers is 105. What is the middle number?
Correct Answer: 21
Rationale: The average of 5 consecutive numbers is 105 / 5 = 21. The middle number is the average when there is an odd number of integers.
6. If the sum of 7 consecutive numbers is 224, what is the highest number?
Correct Answer: 35
Rationale: The average of the 7 numbers is 224 / 7 = 32. Since there are 7 numbers, the middle number is 32. The series is 29, 30, 31, 32, 33, 34, 35. The highest number is 35.
7. Three consecutive odd numbers have a sum of 81. What is the smallest number?
Correct Answer: 25
Rationale: The average of the three numbers is 81 / 3 = 27. This is the middle number. The three consecutive odd numbers are 25, 27, 29. The smallest is 25.
8. If the highest of 5 consecutive numbers is 35, what is the sum of all five numbers?
Correct Answer: 165
Rationale: The five consecutive numbers are 31, 32, 33, 34, 35. The middle number, and the average, is 33. The sum is 33 * 5 = 165.
9. The difference between the lowest and highest of 5 consecutive even numbers is what?
Correct Answer: 8
Rationale: The five consecutive even numbers can be represented as x, x+2, x+4, x+6, x+8. The difference between the highest (x+8) and the lowest (x) is 8.
10. Which of the following represents three consecutive odd numbers?
Correct Answer: x, x+2, x+4
Rationale: This is the correct algebraic representation, as the difference between consecutive odd numbers is always 2.
