Tip #40 to Get a Top SAT Math Score
The second type of sequence question has a repeating pattern, like 1, 2, 3, 1, 2, 3. … To solve this type, write out terms until you see the repeating pattern. Then use the pattern to answer the question.
Let's look at this question:
Solution: Follow the instructions for the sequence that are given in the question, until you notice a repeating pattern. Then use this repeating pattern to answer the question.
- 5, 9, –9, –5, 5, 9, –9, –5, 5
Bingo, there's the pattern. 5, 9, –9, –5, …
So use this pattern to count to the 26th term, which will be 9.
Correct answer: D
Sometimes the pattern does not repeat, but we can determine the amount that it changes between each term and use that to predict a later term. For example, in the pattern 3, 7, 11, 15, 19, …, each term after the first increases by 4. So if we wanted to predict the 105th term, we would add the first term, which is 3, to (104)(4), since there are 104 fours being added to reach the 105th term. 3 + (104)(4) = 419.
These questions are easy once you are familiar with the language. Let's practice.
- 3, 6, 9, 12, …
- In the sequence above, the first term is 3 and every number after that is found by adding 3 to the preceding number. What is the 77th term in the sequence?
- Jenny started a ball at the 15-centimeter mark on a long tape measure. She then rolled it forward 6 centimeters. Before it stopped rolling, the ball settled back toward her one unit. If Jenny continued this pattern for a total of 41 rolls, what mark would the ball reach?
- Jason is writing the letters of his name around the margin of his paper. After he writes the 201st letter, what will be the next letter that he writes?
- 3, 6, –6, …
- The first term in the sequence of numbers shown above is 3. The sequence above continues by adding 3 to every odd-numbered term and multiplying every even-numbered term by –1. For example, the second term is 3 + 3, and the third term is (–1) × 6. What is the 41st term in the sequence?
- A sequence of terms begins with 2x. Each additional term is found by doubling the preceding term. What is the value of the nth term?
- 3, 0, …
- The sequence above continues by subtracting 3 from every odd-numbered term and multiplying every even-numbered term by –1. For example, the second term is 3 – 3, and the third term is (–1) × 0. What is the 167th term in the sequence?
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