Question

Who can answer this have 20 points​

Answer 1

First note that
`A_n` 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

`A_n=2+1*(n-1)`

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

`A_n=2*2^(n-1)\\or\\A_n=2^n`

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

`A_n=A_(n-1)*2-1`

**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

`A_n=25+3*(n-1)`

I hope this helps and if you don't understand any part of my explanation I would gladly help!