To find the sixth, seventh, and eighth terms of the given sequence:

$1, 4, 9, 17, 29, \ldots$

we need to first identify a pattern. Let's calculate the differences between consecutive terms:

• $4 - 1 = 3$
• $9 - 4 = 5$
• $17 - 9 = 8$
• $29 - 17 = 12$

The differences between consecutive terms are increasing by a constant value:

• $5 - 3 = 2$