Question

The fourth term of a sequence is 14. Each term of the sequence is 8 less than the previous term. Which recursive formula represents the situation?

Answer 1

Answer with Step-by-step explanation:

$a_{4}=14$

Each term of the sequence is 8 less than the previous term

⇒ $a_{3}=14+8=22$

⇒ $a_{2}=22+8=30$

⇒ $a_{1}=30+8=38$

In general $a_{n}=a_{n-1}-8,a_{1}=38$

Hence, recursive formula representing the situation is:

$a_{n}=a_{n-1}-8,a_{1}=38$

Answer 2

So

an=an+b

14=4a+b and a=-8

14=-32+b

b= 46

an=-8n+46