By Carla Kirkland, Chan Cleveland

If you run across a question on the Praxis Core exam where you have to solve an arithmetic or geometric sequence, just remember: it’s all about finding regular patterns—and sometimes working backwards.

In the following practice questions, you start by finding a given term in a sequence (easy: just look for the difference between each given term); then you get a word problem where you have to solve a geometric sequence (almost as easy: just plug in the answers!).

Practice questions

  1. What is the seventh term of this sequence?

    5, 9, 13, 17, …

    A. 21
    B. 20
    C. 29
    D. 24
    E. 33

  2. The first term of a geometric sequence is 1. The fifth term is 81. How many times greater is each term, after the first term, than the preceding term?

    A. 2
    B. 9
    C. 4
    D. 18
    E. 3

Answers and explanations

  1. The correct answer is Choice (C).

    After the first term, each term is 4 greater than the previous one. Four terms are shown. The seventh term is three terms past the fourth term, which is 17. That means 4 is added three more times after 17:

    17 + 4 + 4 + 4 = 29

    The seventh term is therefore 29.

  2. The correct answer is Choice (E).

    You can test each choice to see whether it works. If you start with 1 and multiply by the same number repeatedly to get four more terms, with the last one being 81, the number by which each term is multiplied can only be 3. The only choice that works is Choice (E).

    1 × 3 × 3 × 3 × 3 = 81