Question

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

Answer 1

Step-by-step 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

$a_{1} = 4 = = > n = 1 \\ 4 = 2 \times {1}^{2} + b + c = = = = > \\ b + c = 2$

$a_{2} = 7 = = > n = 2 = = = > \\ 7 = 2 \times {2}^{2} + 2 \times b + c = = = > \\ - 1 = 2b + c$

1. b+c=2
2. 2b+c=–1

b=–3, c=5

So the final result is:

$t_{n} = 2 {n}^{2} - 3n + 5$