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

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
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In each term of a sequence, 9 is added to get the next term. If the  [#permalink]

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20 Mar 2013, 14:18
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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

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

Mike

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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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Joined: 24 Jan 2013
Posts: 72
Re: In each term of a sequence, 9 is added to get the next term. If the  [#permalink]

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20 Mar 2013, 14:35
3
2
1rst term + 80 terms = 2 + 9+9+9+9+9+9+9+...+9 (80 times)

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

##### General Discussion
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 312
Re: In each term of a sequence, 9 is added to get the next term. If the  [#permalink]

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20 Mar 2013, 22:10
mikemcgarry wrote:
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:
http://magoosh.com/gmat/2012/sequences-on-the-gmat/

Mike

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
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Posts: 6
Location: United States
Concentration: Finance
WE: Corporate Finance (Non-Profit and Government)
Re: In each term of a sequence, 9 is added to get the next term. If the  [#permalink]

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22 Mar 2013, 13:23
1
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
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Joined: 17 May 2013
Posts: 39
GMAT Date: 10-23-2013
Re: In each term of a sequence, 9 is added to get the next term. If the  [#permalink]

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26 Jul 2013, 06:52
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
Manager
Joined: 03 Jan 2015
Posts: 59
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)
Re: In each term of a sequence, 9 is added to get the next term. If the  [#permalink]

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22 Feb 2015, 19:13
# of terms =[ (last term - first term)/interval] + 1
i.e. [(81-2)/1] + 1 = 80

SVP
Joined: 06 Nov 2014
Posts: 1877
Re: In each term of a sequence, 9 is added to get the next term. If the  [#permalink]

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28 Feb 2015, 11:49
mikemcgarry wrote:
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:
http://magoosh.com/gmat/2012/sequences-on-the-gmat/

Mike

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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Re: In each term of a sequence, 9 is added to get the next term. If the  [#permalink]

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27 Feb 2017, 05:29
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
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Re: In each term of a sequence, 9 is added to get the next term. If the  [#permalink]

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01 Mar 2017, 18:21
1
mikemcgarry wrote:
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

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Intern
Joined: 20 Dec 2018
Posts: 49
Re: In each term of a sequence, 9 is added to get the next term. If the  [#permalink]

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21 Dec 2018, 22:13
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
Re: In each term of a sequence, 9 is added to get the next term. If the   [#permalink] 21 Dec 2018, 22:13
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