Chapter 11.2, Problem 8WE

To determine

To calculate:

The value of $t_{31}$ the following arithmetic sequence:

  $3,11,19,\mathrm{....}$

Answer to Problem 8WE

The value of $t_{31}$ the arithmetic sequence is $270$ .

Explanation of Solution

Given information:

  $3,11,19,\mathrm{....}$

Formula used:

The $n^{th}$ term of an arithmetic sequence is given by the following expression:

  $t_n=t_1+\left(n-1\right)d$

Where,

First term: $t_1$

Common difference: $d$

Calculation:

Consider the sequence as:

  $\begin{array}{l}{t}_1=3\\ t_2=11\\ t_3=19\end{array}$

Now, the common ratio is calculated as:

  $\begin{array}{l}d=t_2-t_1=11-3=8\\ d=t_3-t_2=19-11=8\end{array}$

Know that:

First term: $t_1=3$

Common difference: $d=8$

So, $t_{31}$ term for given arithmetic sequence is calculated as:

  $\begin{array}{l}{t}_{31}=t_1+\left(n-1\right)d\\ t_{31}=3+\left(31-1\right)\left(8\right)\\ t_{31}=3+240\\ t_{31}=270\end{array}$