Chapter 13.7, Problem 45HP

To determine

To find the 100,001st term of the sequence.

Answer to Problem 45HP

700,013

Explanation of Solution

Given:

Sequence: 13, 20, 27, 34, 41,…….

Formula used:

Arithmetic sequence with the first term $a_1$ and the common difference d, the nth term is given by,

  $a_n=a_1+(n-1)d$

Calculation:

In the given sequence, there is a common difference of 7 in each term.

  $\begin{array}{l}13+7=20\hfill \\ 20+7=27\hfill \\ 27+7=34\hfill \\ 34+7=41\hfill \end{array}$

Now, find out the 100,001th term and the first term of the sequence $a_1$ =13.

Substituting in the formula,

  $\begin{array}{c}{a}_{100,001}=13+(100,001-1)7\\ =13+(100,000)7\\ =13+700,000\\ =700,013\end{array}$

Conclusion:

Therefore, the 100,001th term is 700,013