Chapter 3.6, Problem 3AGP

To determine

To find an equation for the nth term of the sequence.

Answer to Problem 3AGP

  $-13n+16$

Explanation of Solution

Given:

Sequence:

  $3,-10,-23,-\mathrm{36...}$

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:

  $-10-3=-13$

Applying above formula,

  $\Rightarrow a_n=a+(n-1)d$

  $\Rightarrow a_n=3(n-1)(-13)$  $[\because a=3,d=-13]$

  $\begin{array}{l}\Rightarrow a_n=(3n-3)(-13)\\ \Rightarrow a_n=-39n+39\end{array}$

So, the nth term of the sequence is $a_n=-39n+39.$

Conclusion:

Therefore, the equation for the nth term of the sequence is $a_n=-39n+39.$