Question

In Exercises \(15-20,\) write the next two apparent terms of the sequence. Describe the pattern you used to find these terms. \(2,5,8,11, \ldots\)

Short answer

The next two terms of the sequence are 14 and 17.

Step-by-step solution

Identify the pattern in the series

Look at the series and identify the pattern that is present. Compare each term to the one before it and see what mathematical operation is done to obtain the next term. In this series (2,5,8,11), the recognized pattern is that each term increases by 3.

Apply the identified pattern to get the next terms

Take the last given term in the series, which is 11, and add the constant pattern (3) to it. So 11 + 3 = 14. This gives us the next term in the series.

Derive the following term

Use the derived term, 14, and apply the same constant pattern which is 'adding 3'. Hence, 14 + 3 = 17. This gives us the next term in the series.

Conclusion

It can be concluded that the next two terms of the series are 14 and 17, as they follow the identified pattern of this arithmetic sequence of adding 3 to the previous term in order to derive the next term.