Chapter 11.5, Problem 5CYU

To determine

Recursive formula for sequence

Answer to Problem 5CYU

The recursive formula is $a_n=a_{n-1}+nd$

Explanation of Solution

Given information:

A sequence $3,8,18,38,78,\mathrm{...}$

Concept used:

A recursive formula is used to express any term of the sequence in terms of the previous term, provided that the first term is given.

Calculation:

In order to find the recursive formula for sequence $3,8,18,38,78,\mathrm{...}$ as shown below

  $\begin{array}{l}{a}_1=3\\ d=8-3=5\\ d=18-8=10\\ a_2=8=3+5=a_1+d\\ a_3=18=8+2d=a_2+2d\end{array}$

So the recursive formula is below:

  $a_n=a_{n-1}+nd$

Thus, the recursive formula is $a_n=a_{n-1}+nd$