GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Sep 2018, 21:44

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In a certain sequence the term an is given by the formula: an=an−1+2n

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 853
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
In a certain sequence the term an is given by the formula: an=an−1+2n  [#permalink]

### Show Tags

15 Jun 2015, 10:39
1
4
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:41) correct 20% (01:42) wrong based on 127 sessions

### HideShow timer Statistics

In a certain sequence the term an is given by the formula:

$$a_n=a_{n−1}+2n-1$$ for all integer $$n>1$$. If $$a_7=49$$, what is $$a_1$$?

A. −1
B. 0
C. 1
D. 2
E. 3

The issue of this question is finding a rule for moving backwards from the 7th term to the 1st term. Isolate an-1:

an = an-1 + 2n - 1

--> an-1 = an − 2n + 1

Plug n into this relation to find the terms preceding the 7th term.

Plug a7=49, and n=7 into an-1 = an − 2n + 1 so:

a6=49−2×7+1=36 (Plugging in a7=49 and n=7)

a5=36−2×6+1=25 (Plugging in a6=36 and n=6)

Do you see the pattern? Each term an equals n2. Hence, a1 is 1.

If you missed the pattern, proceed to calculate a4, a3, a2, and a1:

a4=25−2×5+1=16 (Plugging in a5=25 and n=5)

a3=16−2×4+1=9 (Plugging in a4=16 and n=4)

a2=9−2×3+1=4 (Plugging in a3=9 and n=3)

a1=4−2×2+1=1 (Plugging in a2=4 and n=2)

_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Math Expert
Joined: 02 Aug 2009
Posts: 6800
Re: In a certain sequence the term an is given by the formula: an=an−1+2n  [#permalink]

### Show Tags

15 Jun 2015, 11:03
[quote="reto"]In a certain sequence the term an is given by the formula:

$$a_n=a_{n−1}+2n-1$$ for all integer $$n>1$$. If $$a_7=49$$, what is $$a_1$$?

A. −1
B. 0
C. 1
D. 2
E. 3

..
Hi,
$$a_n=a_{n−1}+2n-1$$....
as we can see that each subsequent term is 2n-1 greater than previous..
so we can straightway find $$a_7$$=(2*1-1)+(2*2-1)+(2*3-1)+(2*4-1)+(2*5-1)+(2*6-1)+(2*7-1)+$$a_1$$=3+5+7+9+11+13+$$a_1$$
$$a_7$$=49=48+$$a_1$$..
or $$a_1$$=1
ans C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Non-Human User
Joined: 09 Sep 2013
Posts: 8150
Re: In a certain sequence the term an is given by the formula: an=an−1+2n  [#permalink]

### Show Tags

28 Aug 2018, 09:07
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In a certain sequence the term an is given by the formula: an=an−1+2n &nbs [#permalink] 28 Aug 2018, 09:07
Display posts from previous: Sort by

# In a certain sequence the term an is given by the formula: an=an−1+2n

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.