Question

Determine the explicit formula for the sequence 4, 7, 14, 25

Answer 1

Explanation:

You already know that we use tn=an²+bn+c for these kinds of sequences:

4, 7, 14, 25, ...

1. 7–4=3
2. 14–7=7

now

7–3=4

So 2a=4===> a=2

`a_(1) = 4 = = > n = 1 \\ 4 = 2 * {1}^(2) + b + c = = = = > \\ b + c = 2`

`a_(2) = 7 = = > n = 2 = = = > \\ 7 = 2 * {2}^(2) + 2 * b + c = = = > \\ - 1 = 2b + c`

1. b+c=2
2. 2b+c=–1

b=–3, c=5

So the final result is:

`t_(n) = 2 {n}^(2) - 3n + 5`