First note that [tex]A_n[/tex] means the nth term in the sequence.
1. First one is a simple arithmetic progression/sequence as the common differences between each two numbers are 1
So the sequence will be
1.) 2,3,4,5,6,7...
And the rule since its +1 each time will be
[tex]A_n=2+1*(n-1)[/tex]
For the nth term of the sequence.
2.This one can be seen as a simple geometric sequence as the common ratio between the number and the number after it is 1:2
So the sequence will be
2.)2,4,8,16,32,64
And the rule since it is *2 each time is a simple exponential function
[tex]A_n=2*2^{n-1}\\or\\A_n=2^n[/tex]
3.This one is tricky but it can be seen that the term is double the term before subtract 1
So the sequence will be
3.)5,9,17,33,65,129
And the rule based on this sequence will be
[tex]A_n=A_{n-1}*2-1[/tex]
**Please note that this rule specifically is written in recursive form as it is a lot more difficult otherwise.
4 This one is similar to problem 1 which is an arithmetic sequence this one just have a common differences of 3 instead of 1.
So the sequence will be
4.)25,28,31,34,37
And the rule based on the sequence will be
[tex]A_n=25+3*(n-1)[/tex]
I hope this helps and if you don't understand any part of my explanation I would gladly help!
