Question

Consider the sequence: 3, 8, 13, 18, 23, ...The recursive formula for this sequence is:an = an-1 + 5In a COMPLETE sentence, explain what an and an-1 represent in the formula. Then find a8 . What do you need to know in order to find a8 ?

Answer 1

Answer:

$a_8=38$

Step-by-step explanation:

Recursive sequence

In a recursive sequence formula, each term $a_n$ is computed as a function of one or more previous terms. In the formula

$a_n=a_{n-1}+5$

n is the number of the term we want to calculate. If n=8, then the formula becomes

$a_8=a_{7}+5$

We can see $a_{n-1}$ is the previous term. It means we need $a_7$ to be able to compute $a_8$. But we also need $a_6$ to compute $a_7$ and so on until some known data is reached. The question provides five terms, $a_5=23.$

$a_6=a_5+5=28$

$a_7=a_6+5=33$

$a_8=a_7+5=38$

$a_8=38$