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In each term of a sequence, 9 is added to get the next term. If the first term is 2, what is the eighty-first term? (A) 632 (B) 695 (C) 713 (D) 722 (E) 731

Quick tip on this type of question: the GMAT is frequently counting on you (pun intended) to miscount and think the answer is off by one iteration in either direction, so the correct answer tends to not be the biggest or smallest you find. This is far from ironclad, but if you find yourself picking the biggest number (in this case E), you've probably fallen for a classic GMAT trap. The solution outlined by johnwesley above is excellent, but a lot of students find themselves doing 81*9+2 = 731 and falling into the trap.

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First term = 2 common difference = 9 Nth term = First term + (N-1)(common difference) So, 81th term = 2 + (81-1)(9) = 2 + 80*9 = 2 + 720 = 722 Hence option D.

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In each term of a sequence, 9 is added to get the next term. If the first term is 2, what is the eighty-first term?

(A) 632 (B) 695 (C) 713 (D) 722 (E) 731

We are given a sequence in which 9 is added to each term and the first term is 2. Let’s list the first few terms:

term 1 = 2 (notice that 2 = 9(0) + 2)

term 2 = 11 (notice that 11 = 9(1) + 2)

term 3 = 20 (notice that 20 = 9(2) + 2)

Thus, term n = 9(n-1) + 2

So the 81st term is 9(80) + 2 = 722

Alternate Solution:

You might recognize this as an arithmetic sequence, with first term 2 and common difference d = 9. To determine the nth term of an arithmetic sequence, we can use the formula a_n = a_1 + (n – 1) * d. We can thus determine the 81st term as follows:

a_81 = 2 + (81 – 1)(9)

a_81 = 2 + (80)(9)

a_81 = 722

Answer: D
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Jeffery Miller Head of GMAT Instruction

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