Question

use inductive reasoning to predict the next three numbers in the pattern (or sequence)
7, 9, 12, 16, 21, 27, ...
the next three numbers in the pattern, in order, are \\(\square\\), \\(\square\\), and \\(\square\\)
(simplify your answers )

Explanation:

Step1: Find the differences between terms

$9-7=2$, $12-9=3$, $16-12=4$, $21-16=5$, $27-21=6$

Step2: Identify the difference pattern

The differences increase by 1 each time: $2,3,4,5,6,...$

Step3: Calculate next term 1

Next difference is $7$, so $27+7=34$

Step4: Calculate next term 2

Next difference is $8$, so $34+8=42$

Step5: Calculate next term 3

Next difference is $9$, so $42+9=51$

Answer:

34, 42, and 51