solve the following sequence 5,0,0,0,3,5

The difference between 5 and 0 is 5. The difference between 0 and 0 is 0. The difference between 0 and 0 is 0. The difference between 0 and 3 is -3. The difference between 3 and 5 is 2. Notice that the differences alternate between positive and negative values. Let's describe the pattern: Start with 5. Subtract 5 (resulting in 0). Subtract 0 (resulting in 0). Add 3 (resulting in -3). Add 2 (resulting in -1). Now, you can extend the pattern: Subtract 1 from -1, which results in -2. Subtract 1 from -2, which results in -3. Subtract 1 from -3, which results in -4. Subtract 1 from -4, which results in -5. Subtract 1 from -5, which results in -6. So, the extended sequence is: 5, 0, 0, 0, 3, 5, -1, -2, -3, -4, -5, -6, ...