Question

use inductive reasoning to predict the next three numbers in the pattern.
4, 7, 11, 18, 29, 47, ...

predict the next three numbers in the pattern.
4, 7, 11, 18, 29, 47, \square, \square, \square

Explanation:

Step1: Identify the pattern

Each term = sum of two prior terms.
$4+7=11$, $7+11=18$, $11+18=29$, $18+29=47$

Step2: Calculate 7th term

Sum of 5th and 6th terms.
$29+47=76$

Step3: Calculate 8th term

Sum of 6th and 7th terms.
$47+76=123$

Step4: Calculate 9th term

Sum of 7th and 8th terms.
$76+123=199$

Answer:

76, 123, 199