BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Sequence

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 42
Joined: Sat Apr 12, 2008 8:51 am
Thanked: 1 times
by gibran » Thu May 15, 2008 6:03 am
The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence?
A. 72
B. 74
C. 75
D. 78
E. 80

Please help me to solve this one.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Junior | Next Rank: 30 Posts
Posts: 26
Joined: Thu May 15, 2008 1:02 am
Thanked: 1 times

by m51v50 » Thu May 15, 2008 7:03 am
The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence?
A. 72
B. 74
C. 75
D. 78
E. 80

My approach:
According to the formula:
a5 = an-4 = a1=2. Meaning that the cycle repeats after every four number.
And the sum of a cycle =2-3+5-1=3
So, 97/4 = 24 full cycle.
So sum will be 24*3 =72+the first term=72+2=74.
Have 790 or die
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 104
Joined: Wed Feb 13, 2008 1:44 pm
Thanked: 8 times

by punit.kaur.mba » Thu May 15, 2008 7:10 am
According to me, the answer is 74 (B). This is one way you could solve it -

Since the given sequence is

2, -3, 5 , 1,

From the formula given

a5 = a(5-4)=a1=2

Similarly a6=a2 (-3) , a7=a3 (5), a8=a4 (-1)

So the sequence of first four numbers is repeating -
Hence the infinite sequence looks like this:

2, -3, 5, -1, 2, -3, 5, -1, 2, -3, 5, -1 and so on...

Now to find out the sum, you can group the pattern like this

(2, -3, 5 , -1) + (2, -3, 5, -1) + ...

Find sum of each group -
(3) + (3) + ....


Since the pattern is repeating after every four numbers, and since 96 is multiple of 4, the new pattern will start from 97th number.

97th number is 2

97 = 4 * n + 1

n=24



So the sum of 97 terms is

(3) * 24 + 2 = 72 + 2

Let me know if you have quest!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 631
Joined: Mon Feb 18, 2008 11:57 pmFollowed by: 3 members
Thanked: 29 times

by netigen » Thu May 15, 2008 11:18 am
at least make the effort to post the question correctly

what is an = an-4

is it an = (an-4)
or is it an = a(n-4)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1