SAT Math Multiple Choice Question 739: Answer and Explanation

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Question: 739

4. A: 2, 7, 12, 17, 22, . . .

B: 5, 15, 25, 35, 45, . . .

Two sequences, A and B, follow the patterns shown above. If the nth term of sequence A is 72, what is the nth term of sequence B?

  • A. 125
  • B. 135
  • C. 145
  • D. 155

Correct Answer: C

Explanation:

C

Advanced Mathematics (sequences) MEDIUM-HARD

The "brute force" method is to write out sequence A until you reach 72, and see which element in sequence B "matches up" to it. But first we must determine the rule for each sequence. A little guessing and checking should confirm that sequence A follows the "add 5" rule, and sequence B follows the "add 10" rule.

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A more elegant method, however, is to find the formulas for the nth term of A and the nth term of B. This would be a much more efficient method, also, if it takes a while for 72 to appear in set A. If you recall the general formula for the nth term of an arithmetic sequence (an = a1 + (n - 1)d), then it's straightforward to see that the formula for A is an = 2 + (n - 1)5 = 5n - 3 and the formula for B is bn = 5 + (n - 1)10 = 10n - 5. Since we're looking for where the number 72 appears in set A, we can solve 5n - 3 = 72 to find n = 15, then insert this value for n into the formula for B: b15 = 10(15) - 5 = 145.

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