Sequences and Series · Overview

Sequences and Series

Sequence questions give you a list of numbers that follows a rule and ask for a term far down the list, the rule itself, or the sum of many terms. The two main kinds are arithmetic sequences, which add the same number each time, and geometric sequences, which multiply by the same number. You will also see recursive rules, where each term is built from the one before it, and repeating patterns, such as the digits of a repeating decimal or the powers of ii.

Every question is multiple choice with four options. Most are short and pure, but some are word problems about rows of seats, savings or growth. The wrong choices come from a small set of slips: counting terms instead of steps, adding a ratio instead of multiplying, using a term in place of a sum, and miscounting a remainder.

How often it appears

Sequences sit in Number and Quantity, part of Preparing for Higher Math, which makes up about 80% of the ACT Math section. Number and Quantity is about 10–12% of the section, so on a 45-question test expect about 5 questions from it, and a sequence or pattern question is a regular visitor among them.

You have 50 minutes for 45 questions, about 67 seconds each. Once you count steps carefully, these questions are quick, so they are a good place to bank time.

The question you’ll see

In an arithmetic sequence, the 4th term is 19 and the 10th term is 49. What is the 25th term of the sequence?

In this module

  1. Overview Paid
  2. Arithmetic sequences Paid
  3. Geometric sequences Paid
  4. Sums of arithmetic and geometric series Paid
  5. Recursive rules and repeating patterns Paid
  6. Strategy summary Paid
  7. Mastery quiz Paid
  8. Pace check Paid