Chapter 7.10, Problem 7CYU

To determine

The recursive formula from the given explicit formula.

Answer to Problem 7CYU

The recursive formula is $a_1=13$ , $a_n=a_{n-1}+5$ , $n\ge 2$

Explanation of Solution

Given information: The explicit formula given $a_n=5n+8$ .

Calculation:

The formula given $a_n=5n+8$ .

By plugging in n=1, first term $a_1=5(1)+8=5+8=13$ .

When n=2, second term $a_2=5(2)+8=10+8=18$ .

When n=3, third term $a_3=5(3)+8=15+8=23$ .

When n=4, fourth term $a_4=5(4)+8=20+8=28$ .

So the sequence becomes 13, 18, 23, 28,….

We can write it as,

  $\begin{array}{l}{a}_2=18=13+5=a_1+5\\ a_3=23=18+5=a_2+5\\ a_4=28=23+5=a_3+5\end{array}$

  $\therefore$ we can write, $a_n=a_{n-1}+5$ .

So the recursive formula we can write, $a_1=13$ , $a_n=a_{n-1}+5$ , $n\ge 2$ .