Number Dojo Level: 61
Adding a sequence:
- First, determine how many numbers are in the sequence.
- If there are an odd number of terms, multiply that number by the middle term.
- If there are an even number of terms, multiply that number by the average of the middle two terms.
- There are 5 terms, which is odd (not strange--an odd number).
- 10 is the middle term. 5 x 10 = 50.
- This works because the average of the first and last terms (4 & 16) is equal to the middle term (10). The average of the second and second-to-last terms (7 & 13) is also equal to the middle term, etc.
- There are 7 terms, which is an odd number.
- The middle term is 11. 7 x 11 = 77.
- There are 6 terms--an even number.
- Look at the middle 2 terms (8 & 10) and take the average (9).
- Multiply the # of terms (6) by 9 to get 54.
- There are 4 terms--an even number.
- The average of the middle 2 terms (28 & 18) is 23. 4 x 23 = 92.
- Notice that the average of the first & last terms (38 & 8) is also 23. This is helpful when some of the terms are left out of the question and replaced by an ellipsis (...).
- This sequence consists of multiples of 3. Based on the last number being 27, you can determine that there are 9 terms.
- Since you can't easily tell what the middle term is, just take the average of the first and last terms (3 & 27), which is 15. 9 x 15 = 135.