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Subject Test Math 2

Question 23 of 28

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SAT Subject Test

For some real number t, the first three terms of an arithmetic sequence are 2 t comma space5 t minus 1 comma spaceand 6 t plus 2. What is the numerical value of the fourth term?

Select an Answer

4

Correct Answer: 
No

8

Correct Answer: 
No

10

Correct Answer: 
No

16

Correct Answer: 
No

19

Correct Answer: 
Yes

The correct answer is E.

To determine the numerical value of the fourth term, first determine the value of t and then apply the common difference.

Since 2 t comma 5 t minus 1, and 6 t plus 2 are the first three terms of an arithmetic sequence, it must be true that left parenthesis 6 t plus 2 right parenthesis minus left parenthesis 5 t minus 1 right parenthesis equals left parenthesis 5 t minus 1 right parenthesis minus 2 t, that is, t plus 3 equals 3 t minus 1. Solving t plus 3 equals 3 t minus 1 for t gives t equals 2. Substituting 2 for t in the expressions of the three first terms of the sequence, one sees that they are 4, 9, and 14, respectively. The common difference between consecutive terms for this arithmetic sequence is 5 equals 14 minus 9 equals 9 minus 4, and therefore, the fourth term is 14 plus 5 equals 19.

Question Difficulty: 
hard