# SAT Math Multiple Choice Question 621: Answer and Explanation

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**Question: 621**

**6.** The *n*th term of a sequence is given by the expression *bn* + 4, where *b* is a positive constant. Which of the following is necessarily equal to *b*?

- A. the value of the first term
- B. the difference between the fourth term and the third term
- C. the average (arithmetic mean) of the first three terms
- D. the ratio of the second term to the first term

**Correct Answer:** B

**Explanation:**

**B**

**Advanced Mathematics (sequences) MEDIUM**

Let's choose a value, like *b* = 2, for our positive constant. This gives us an expression of 2*n* + 4 for the *n*th term of the sequence. Substituting *n* = 1, *n* = 2, *n* = 3, etc. gives us a sequence of 6, 8, 10, 12, 14, and so on. Choice (A) is clearly incorrect, because the first term of this sequence is not 2. Choice (C) is also incorrect because the average of the first three terms is (6 + 8 + 10)/3 = 8, not 2. Choice (D) is also incorrect because the ratio of the second term to the first is 8/6 = 4/3. Only choice (B), the difference between the fourth term and the third term, 12 - 10, gives us a value of 2.