Chapter 0, Problem 37P

To determine

To write: the verbal rule to describe the pattern and find the 10^th term.

Answer to Problem 37P

10th term of this sequence is 51.

Explanation of Solution

Given: $6,11,16,21,\mathrm{...}$

Calculation:

Observe the sequence,

  $\begin{array}{l}{1}^{st}\text{term}=5+1\\ 2^{nd}\text{term}=\left(5\times 2\right)\text{+1 }\\ 3^{rd}\text{term}=\left(5\times 3\right)\text{+1 }\\ 4^{th}\text{term}=\left(5\times 4\right)\text{+1 }\end{array}$

Thus, the $n^{th}$ term is given by $\left(5+n\right)+1.$

Therefore, the value of the term is equal to one more than five times the term number.

Now, find the 10th term in this sequence.

  $\begin{array}{l}{10}^{th}\text{term}=\left(5\times 10\right)+1\hfill \\ =50+1\hfill \\ =51\hfill \end{array}$

Conclusion:

Hence, 10th term of this sequence is 51.