Chapter 4.6, Problem 52E

To determine

To describe: The arithmetic sequence in a real life

Answer to Problem 52E

The arithmetic sequence in a real life is $125,150,175,\mathrm{...}$

Explanation of Solution

Calculation:

Consider there are 125 passengers in the first carriage, 150 passengers in the second carriage and 175 passengers in the third carriage, and so on.

Also, the first term of the sequence is $a_1=125$ , second term of the sequence is $a_2=150$ and third term of the sequence is $a_3=175$ .

Now, the difference d is

  $\begin{array}{l}d=175-150\hfill \\ =25\hfill \end{array}$

And

  $\begin{array}{l}d=150-125\hfill \\ =25\hfill \end{array}$

As the difference is same, the sequence is arithmetic.

Carriage, x	1	2	3
People, y	125	150	175

Conclusion:

Therefore, the arithmetic sequence in a real life is $125,150,175,\mathrm{...}$