Chapter 12.2, Problem 36AYU

In Problems 31-38, find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for the sequence. Find a formula for the nth term.

$12thtermis4;18thtermis28$

To determine

To find: The $1^{st}$ term, common difference, recursive formula and formula for $n$th term.

Answer to Problem 36AYU

1. $a_1=-40, d=4$

2. $a_n=a_{n-1}+4$

3. $a_n=4n-44$

Explanation of Solution

Given:

${12}^{th}$ term is 4 and ${18}^{\text{th}}$ term is 28.

Formula used:

Formula for $n^{th}$ term:

$a_n=a_1+\left(n-1\right)d$   Eq (1)

$a_n=a_{n-1}+d$   Eq (2)

Calculation:

From Eq (1) and given data,

$a_{12}=a_1+11d=4$

$a_{18}=a_1+17d=28$

Solving above two equations,

$d=4$; $a_1=40$

From Eq(2), we get the recursive formula,

$a_n=a_{n-1}-4$

The formula for $n^{th}$ term is

$a_n=a_1+\left(n-1\right)d=-40+\left(n-1\right)\left(4\right)=4n-44$