Chapter 12.2, Problem 29AYU

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.

$8thtermis8;20thtermis44$

To determine

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

Answer to Problem 29AYU

1. $a_1=-13, d=3$

2. $a_n=a_{n-1}+3$

3. $a_n=3n-16$

Explanation of Solution

Given:

$8^{th}$ term is 8 and $20\text{th}$ term is 44.

Formula used:

Formula for nth 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,

$a_8=a_1+7d=8$

$a_{20}=a_1+19d=44$

Solving above two equations,

$d=3$; $a_1=-13$

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

$a_n=a_{n-1}+3$

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

$a_n=a_1+\left(n-1\right)d=-13+\left(n-1\right)3=3n-16$