In each term of a sequence, 9 is added to get the next term. If the

Question

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

For more on sequences, as well as a complete explanation of this question, see:
https://magoosh.com/gmat/2012/sequences-on-the-gmat/

Mike :-)

johnwesley · Accepted Answer

1rst term + 80 terms = 2 + 9+9+9+9+9+9+9+...+9 (80 times)

2 + (9 x 80) = 2 + 720 = 722

Answer D

VeritasPrepRon · Answer

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.

Hope this helps!
-Ron

husker2010 · Answer

Xo = 2
X1 = Xo + 9 = 2 + 9
X2 = X1 + 9 = (2 + 9) + 9
X3 = X2 + 9 = ((2+ 9) +9) +9

Xn = 2 + 9n
X80 = 2 + 9(80)

X80 = 722
D

GMAT40 · Answer

There is formula where you can find the nth term.

a + (n-1)d

a = first term = 2
d = common difference = 9

so for 81th term

2 + (81-1)9 = 722

thorinoakenshield · Answer

# of terms =  + 1
i.e.   + 1 = 80

(80*9)+2 = ANSWER

OptimusPrepJanielle · Answer

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. -- Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course

KrishnakumarKA1 · Answer

First term is 2
Second term is 2 + 9 = 2 +(2-1)9
Third term is 2 +9 +9 = 2 +(3-1)9
.
.
.
.
81st term is 2 +(81-1)*9 = 722. Option D

JeffTargetTestPrep · Answer

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

masoomjnegi · Answer

Clearly the pattern given in the question is that of an A.P. with first term = 2 and common difference = 9.
So, 81st term = p = a + (n – 1)d = 2 + (81 – 1)9 = 2 + (80)9 = 722

In each term of a sequence, 9 is added to get the next term. If the

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