Chapter 8, Problem 14SGR

To determine

To write: an equation and find the ${\text{47}}^{\text{th}}$ term.

Answer to Problem 14SGR

The equation that describe the sequence $6,10,14,18,\mathrm{...}$ is $t=4n+2$

The value of ${\text{47}}^{\text{th}}$ term of sequence is 190

Explanation of Solution

Given:

Consider the sequence: $6,10,14,18,\mathrm{...}$

Calculation:

In the sequence, the terms have common difference of 4.

And, a term is 2 more than four times the term number. It means that the equation of sequence is:

  $t=4n+2$

Now, in order to calculate the value of ${\text{47}}^{\text{th}}$ term of the sequence, put the value of $n=47$ in the equation.

  $\begin{array}{c}t=4\left(47\right)+2\\ =188+2\\ =190\end{array}$

Conclusion:

Therefore, the equation that describe the sequence $6,10,14,18,\mathrm{...}$ is $t=4n+2$

And, the value of ${\text{47}}^{\text{th}}$ term of sequence is 190