$1<\quad$ Use differences to find a pattern in the sequence. $2,6,14,31,62,112,186$ Assuming that the pattern continues, the eighth term should bej

Step 1 ：Given the sequence \(2, 6, 14, 31, 62, 112, 186\)

Step 2 ：Calculate the differences between consecutive terms to get \(4, 8, 17, 31, 50, 74\)

Step 3 ：Calculate the second differences to get \(4, 9, 14, 19, 24\)

Step 4 ：Notice that the second differences are increasing by 5 each time, suggesting a cubic sequence

Step 5 ：Predict the next second difference to be \(29\) by adding 5 to the last second difference

Step 6 ：Calculate the next difference by adding the predicted second difference \(29\) to the last difference \(74\) to get \(103\)

Step 7 ：Calculate the next term by adding the next difference \(103\) to the last term \(186\) to get \(289\)

Step 8 ：\(\boxed{289}\) is the eighth term in the sequence