Leunal sequence
2-9-20.. -141
To understand the Leunal sequence and find the next number in the given sequence (2-9-20.. -141), we need to observe the pattern and make some calculations.
The Leunal sequence follows the pattern of subtracting consecutive increasing square numbers from a given starting number.
Let's break it down step by step:
1. Starting with the given number 2.
2. The first square number is 1 (1^2 = 1), so subtract 1 from 2: 2 - 1 = 1.
3. The second square number is 4 (2^2 = 4), so subtract 4 from 1: 1 - 4 = -3.
4. The third square number is 9 (3^2 = 9), so subtract 9 from -3: -3 - 9 = -12.
5. The fourth square number is 16 (4^2 = 16), so subtract 16 from -12: -12 - 16 = -28.
6. The fifth square number is 25 (5^2 = 25), so subtract 25 from -28: -28 - 25 = -53.
7. The sixth square number is 36 (6^2 = 36), so subtract 36 from -53: -53 - 36 = -89.
8. The seventh square number is 49 (7^2 = 49), so subtract 49 from -89: -89 - 49 = -138.
9. The eighth square number is 64 (8^2 = 64), so subtract 64 from -138: -138 - 64 = -202.
Therefore, the next number in the Leunal sequence after -141 is -202.
To find subsequent terms in the sequence, you would continue the pattern by subtracting the next square number (81 for the ninth term, 100 for the tenth term, and so on) from the previous term.