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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
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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
[Reveal] Spoiler: OA

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Mike McGarry
Magoosh Test Prep

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

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

Veritas Prep GMAT Instructor
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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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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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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
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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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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
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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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22 Dec 2014, 09:55
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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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22 Feb 2015, 19:13
# of terms =[ (last term - first term)/interval] + 1
i.e. [(81-2)/1] + 1 = 80

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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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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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29 Sep 2016, 03:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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
Target Test Prep Representative
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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
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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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Re: In each term of a sequence, 9 is added to get the next term. If the   [#permalink] 01 Mar 2017, 18:21
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