To find the pattern in the given sequence, let's look at the differences between consecutive terms:
26 - 7 = 19
63 - 26 = 37
124 - 63 = 61
215 - 124 = 91
342 - 215 = 127
We can notice that the differences between consecutive terms are increasing by 18 each time: 19, 37, 61, 91, 127.
Now, let's look at the second differences:
37 - 19 = 18
61 - 37 = 24
91 - 61 = 30
127 - 91 = 36
We can see that the second differences are increasing by 6 each time: 18, 24, 30, 36.
So, based on this pattern, we can predict that the next second difference would be 42 (36 + 6).
Now, let's calculate the next difference:
127 + 42 = 169
And finally, let's add this difference to the last term in the sequence:
342 + 169 = 511
Therefore, the next term in the sequence is 511.
Comparing this with the given options:
A) 481 - Incorrect
B) 511 - Correct
C) 391 - Incorrect
D) 421 - Incorrect
The correct answer is option B) 511.