Use differences to find a pattern in the sequence.
1,1,11,36,81,151,251
Assuming the pattern continues, the eight term should be.
To find a pattern in the given sequence, we can start by looking at the differences between consecutive terms.
The differences in the sequence are:
1, 10, 25, 45, 70, 100
Now, let's take a closer look at these differences:
1, 10, 25, 45, 70, 100
We can observe that the differences are increasing consecutively by adding an odd number each time. Specifically, the differences increase by 9, then 15, then 20, then 25, and so on.
To continue the sequence, we can use this pattern of increasing differences. The next difference will be 100 + 30 = 130. Adding this difference to the last term of the original sequence, 251, gives us the next term of the sequence:
251 + 130 = 381
Therefore, if the pattern continues, the eighth term of the sequence should be 381.
Please note that this is assuming the given pattern continues consistently. It's important to remember that patterns in sequences can sometimes change unexpectedly.