We know that our formula for arithmetic sequence sums is: If she meets her goal and sells boxes of cookies for a total of 10 days, how many boxes total did she sell?Īs with almost all sequence questions on the ACT, we have the choice to use our formulas or do the problem longhand. On her first day, she sells 12 boxes of cookies, and she intends to sell 5 more boxes per day than on the day previous. The difference between each term-found by dividing any neighboring pair of terms-is called $r$, the common ratio.Ģ12, -106, 53, -26.5, 13.25… is a geometric sequence in which the common ratio is $-/2)$ is completely up to you.Īndrea is selling boxes of cookies door-to-door. We can find this $d$ by again subtracting pairs of numbers in the sequence.Ī geometric sequence is a sequence of numbers in which each successive term is found by multiplying or dividing by the same amount each time. is an arithmetic sequence in which the common difference is -3.25. We can find the $d$ by subtracting any two pairs of numbers in the sequence-it doesn’t matter which pair we choose, so long as the numbers are next to one another.ġ2.75, 9.5, 6.25, 3, -0.25. 5, -1, 3, 7, 11, 15… is an arithmetic sequence with a common difference of 4. The difference between each term-found by subtracting any two pairs of neighboring terms-is called $d$, the common difference. Only once you feel you have a solid handle on the more common types of math topics on the test-triangles (comng soon!), integers, ratios, angles, and slopes-should you turn your attention to the less common ACT math topics like sequences.įor the purposes of the ACT, you will deal with two different types of sequences-arithmetic and geometric.Īn arithmetic sequence is a sequence in which each term is found by adding or subtracting the same value.
What does this mean for you? Because you may not see a sequence at all when you go to take your test, make sure you prioritize your ACT math study time accordingly and save this guide for later studying. In fact, sequence questions do not even appear on every ACT, but instead show up approximately once every second or third test. Take note that sequence problems are rare on the ACT, never appearing more than once per test. This will be your complete guide to ACT sequence problems-the various types of sequences there are, the typical sequence questions you’ll see on the ACT, and the best ways to solve these types of problems for your particular ACT test taking strategies. We will go through each method, and the pros and cons of each, to help you find the right balance between memorization, longhand work, and time strategies. There are several different ways to find the answers to the typical sequence questions-”What is the first term of the sequence?”, “What is the last term?”, “What is the sum of all the terms?”-and each has its benefits and drawbacks.
Whether new term in the sequence is found by an arithmetic constant or found by a ratio, each new number is found by a certain rule-the same rule-each time. Sequences are patterns of numbers that follow a particular set of rules. Let's start with a few simple definitions of the concepts that we will repeatedly use.Īrithmetic-Geometric Progression (AGP): This is a sequence in which each term consists of the product of an arithmetic progression and a geometric progression.
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