SAT Math Multiple Choice Practice Question 190: Answer and Explanation
14. A sequence has 9 as its second term and 17 as its fourth term. If each term is a constant amount greater than the previous term, determine the 13th term of the sequence.
Correct Answer: C
C. The key to this problem is determining what the constant difference between the terms is. You know the second and fourth terms, so the difference between them (17 - 9 = 8) is twice the value of the constant difference, meaning that the constant difference is 4. From here, you can either make a list of the terms until you get to the 13th term (remember that 9 is the second term, not the first!), or you can use the formula you know from Chapter 12: The nth term = the first term + (n - 1)d, where d is the difference between the terms in the sequence. For this question, n is 13, d is 4, and you can get the first term by subtracting the constant difference, 4, from the second term: 9 - 4 = 5. Using the equation, the 13th term is 5 + (13 - 1)4 = 5 + (12)4 = 5 + 48 = 53.