SAT Math: Sequence Problems

SAT Question of the Day

The SAT question of the day is a Sequences question that tests your ability to recognize patterns.

Read the question carefully:  This will keep you from making mistakes.  You know that you have the numbers 3, 6, 11, and 18.  These numbers are all related by the same formula.

Identify the bottom line:   What is the formula that gives the nth number in the sequence for all positive integers n?  Notice that n is not a number that results from the pattern; n is the location (the position) of the number in the sequence.  Write out the n for each number that you have been given.

3,   6,   11,   18

n = 1,   2,    3,    4

Assess your options:  You could try to find the pattern between all of these numbers on your own, but that will take a lot of trial and error.  Instead, notice that this is a "Which of the following" question.  Use your Knowsys strategies and simply eliminate the answer choices that do not work.

Attack the problem

All you have to do is plug in a number for the variable n and make sure that the result is the correct number in your list.   You could plug in n = 1 and eliminate any choices that do not result in 3.  However, one of your tips when working with sequences is that the biggest numbers will be the hardest to fit into a pattern.  If you start with the smallest number, you will only be able to eliminate two answer choices, and then you will have to plug in more numbers.  Start with your biggest numbers, n = 4, and eliminate any choices that do not give you 18.

(A) 2n = 2(4) = 8     Eliminate this choice.

(B)  2n + 1 = 2(4) + 1 = 9     Eliminate this choice.

(C) 3n = 3(4) = 12     Eliminate this choice.

(D) n^2 + 1 = (4)^2 + 1 = 17     Eliminate this choice.

(E) n^2 + 2 = (4)^2 + 2 = 18     This answer works!

Loop Back: You eliminated all but one answer!  You do not even need to plug in any other numbers to see if (E) has the correct pattern.  All of the other numbers that you were given must also fit in this pattern.

The correct answer is (E).

On sat.collegeboard.org, 46% of the responses were correct.

ACT Question of the Day

The ACT question of the day is a Reading question that has already been addressed on this blog: click here to see an explanation.

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