Sequences / Quadratic Sequences

Question 1

What does the letter n represent

Answer 1

The position of a number

Question 2

How do you solve this sequence

3 5 9 11 13

Answer 2

Each number has a difference of 2 so we know its 2n

Now multiply the position by 2 and find the difference

1× 2 = 2
3-2 = 1

2×2 = 4
5-4 = 1

The answer is 2n+1

Question 3

How do you solve this quadratic sequence

-2 7 22 43 70

Answer 3

First find the difference between each of these numbers

9 5 21 27

Next find the difference between these numbers - 6
Divide this number by 2
We now have 3n^2
Write out the square numbers 1 4 9 16
Then times them by 3

3 12 27 48

Now find the diference between these and the original numbers

-2-3 = -5
7-12 = -5
22-27 = -5

So the sequence is
3n^2-5