Tip #39 to Get a Top SAT Math Score

There is a complex formula for sequence questions that you may or may not have used in school, but on the SAT we do not need it. There are only two kinds of sequence questions on the SAT (Skills 39 and 40). The first requires you to write out a bunch of terms and do something with them, such as find the sum or average.

Solution: Write out the first 5 terms of the sequence, following the directions: 3, 7, 11, 15, 19. Then find the sum by adding these five terms.

Correct answer: 55

That was so easy to explain that I have some room left. So, here's Brian's Math Magic Trick #2.

Example Problems

Easy

3, 6, 12, 24, …

1. In the sequence above, the first term is 3 and every number after that is found by doubling the preceding number. What is the 7th term in the sequence?
   1. 48
   2. 96
   3. 192
   4. 240
   5. 384
   112, 54, 18, …
2. In the sequence above, each number after the first is of the preceding term. What is the 6th term of the sequence?
3. What is the greatest of four consecutive prime integers, if the least is integer is 11 ?

Medium

4. The first term in a sequence is 12, and the second term is 8. The third term and each term after the third are the average of the preceding two terms. What is the value of the first term in the sequence that is an odd number?
5. In a given sequence, the first term is 1, and every number after the first is found by adding 3 and then doubling the result. What is average of the first six terms in the sequence?
   1. 10.5
   2. 15.75
   3. 39
   4. 67.5
   5. 405
6. Sora 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 would settle back toward her one unit. She continued this pattern until the ball reached the 60-centimeter mark. How many times did Sora roll the ball?
   1. 10
   2. 9
   3. 8
   4. 7
   5. 6