use inductive reasoning to predict the next three number in the patterns

3,4,7,11,18,29

I noticed the Fibonacci Number property, that is, adding the last two numbers produces the next number.

note:
3+4=7
4+7=11
11+7=18
etc

Find the letter that will be entry ​#130


in the sequence. A,G,G,G,G,A,G,G,G,G,G


not enough to go on. All we have is

A, 4G's, A, 5G's

no telling how many G's we are expecting between the A's. 4,5 ... is not much info.

42,57,74

2 4 6 8 10 12

To use inductive reasoning to predict the next three numbers in the pattern, we need to observe the pattern and look for a rule or pattern that connects the given numbers.

From the given sequence: 3, 4, 7, 11, 18, 29, we can see that each subsequent number is obtained by adding a certain value to the previous number. Let's find the difference between each consecutive pair of numbers:

4 - 3 = 1
7 - 4 = 3
11 - 7 = 4
18 - 11 = 7
29 - 18 = 11

From this observation, we can see that the differences between consecutive numbers appear to be increasing by 2 every time. So, we can extend the pattern by adding 11 + 2 to the last difference, which is 11.

11 + 2 = 13

Next, we need to determine the next number by adding 13 to the last number of the given sequence, which is 29.

29 + 13 = 42

Therefore, the predicted next three numbers in the pattern are 42, 55, and 68.