Chapter 3.6, Problem 42PFA

a.

To determine

To determine the formula for the nth term.

Answer to Problem 42PFA

  $31-6n$

Explanation of Solution

Given:

First three terms of a sequence:

  $25,19,13$

Formula used:

nth term of any arithmetic progression is given by the formula:

  $t_n=a+(n-1)d$

  $t_n=$ nth term

  $a=$ The first term of the arithmetic progression

  $d=$ The common difference of the arithmetic progression

Calculation:

The common difference of the arithmetic progression is:

  $19-25=-6$

Applying the above formula,

  $\Rightarrow a_n=a+(n-1)d$

  $\Rightarrow a_n=25+(n-1)(-6)$  $[\because a=25\&d=-6]$

  $\begin{array}{l}\Rightarrow a_n=25-6n+6\\ \Rightarrow a_n=31-6n\end{array}$

The required nth term formula of the sequence is $a_n=31-6n$ .

Conclusion:

Therefore, the required formula is $31-6n$ .

b.

To determine

To determine the 9^thterm.

Answer to Problem 42PFA

  $-23$

Explanation of Solution

Given:

First three terms of a sequence:

  $25,19,13$

Formula used:

nth term of any arithmetic progression is given by the formula:

  $t_n=a+(n-1)d$

  $t_n=$ nth term

  $a=$ The first term of the arithmetic progression

  $d=$ The common difference of the arithmetic progression

Calculation:

For the 9^th term of the sequence put $n=9,$

  $a_9=31-6\times 9=31-54=-23$

Conclusion:

The required 9^th term of the sequence is $-23$ .