Last visit was: 14 Nov 2024, 09:37 It is currently 14 Nov 2024, 09:37

Close

GRE Prep 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
Your Progress

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

Practice
Pays

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12188 [4]
Given Kudos: 136
Send PM
Retired Moderator
Joined: 07 Jan 2018
Posts: 739
Own Kudos [?]: 1444 [3]
Given Kudos: 93
Send PM
Intern
Intern
Joined: 01 Dec 2021
Posts: 4
Own Kudos [?]: 1 [0]
Given Kudos: 2
Send PM
Verbal Expert
Joined: 18 Apr 2015
Posts: 29958
Own Kudos [?]: 36219 [0]
Given Kudos: 25903
Send PM
Re: The sequence of numbers t_1, t_2, [#permalink]
Expert Reply
Tara007 wrote:
Can someone explain in detail please?


see above sir
Intern
Intern
Joined: 01 Dec 2021
Posts: 4
Own Kudos [?]: 1 [0]
Given Kudos: 2
Send PM
Re: The sequence of numbers t_1, t_2, [#permalink]
Carcass yes, I saw but the sequence repeats after 5 terms not 6 ... Also, can we not use Number of terms x Median formula here? Thanks!
Verbal Expert
Joined: 18 Apr 2015
Posts: 29958
Own Kudos [?]: 36219 [0]
Given Kudos: 25903
Send PM
Re: The sequence of numbers t_1, t_2, [#permalink]
Expert Reply
Tara007 wrote:
Carcass yes, I saw but the sequence repeats after 5 terms not 6 ... Also, can we not use Number of terms x Median formula here? Thanks!


No Sir

the pattern above is starting all over again at 6th term which is zero The above explanation is correct.

No sir

We do not have information about the median. The question is conceived to test a recursive sequence
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12188 [1]
Given Kudos: 136
Send PM
The sequence of numbers t_1, t_2, [#permalink]
1
GreenlightTestPrep wrote:
The sequence of numbers \(t_1\), \(t_2\), \(t_3\), . . . , \(t_n\), . . . is defined by \( t_ n = t_{n-1} - t_{n-2}\) for \(n > 2\).

If \(t_ 1 = 1\) and \(t_ 2 = 1\), What is the sum of the first \(50\) terms of this sequence?

A) \(-2\)

B) \(-1\)

C) \(0\)

D) \(1\)

E) \(2\)

Let’s first list some terms to see if we can spot a pattern…
\(t_ 1 = 1\)
\(t_ 2 = 1\)
\(t_ 3 = t_2 – t_1 = 1 – 1 = 0\)
\(t_ 4 = t_3 – t_2 = 0 – 1 = -1\)
\(t_ 5 = t_4 – t_3 = (-1) – 0 = -1\)
\(t_ 6 = t_5 – t_4 = (-1) – (-1) = 0\)
\(t_ 7 = t_6 – t_5 = 0 - (-1) = 1\)
\(t_ 8 = t_7 – t_6 = 1 - 0 = 1\)
\(t_ 9 = t_8 – t_7 = 1 - 1 = 0\)
\(t_ {10} = t_9 – t_8 = 0 - 1 = -1\)
.
.
.
At this point, we can see that the pattern repeats itself after 6 terms
In other words, the six terms from \(t_1\) to \(t_6\) are exactly the same as the six terms from \(t_7\) to \(t_{12} \) (as well as the six terms from \(t_{13}\) to \(t_{18}\), etc)

The sum of the first six terms \(= 1 + 1 + 0 + (-1) + (-1) + 0 = 0\)
So, the sum of the next six terms after that \(= 0\)
And the sum of the next six terms after that \(= 0\)
Etc.

There are 8 sets of six terms from \(t_1\) to \(t_{48}\), which means the sum of the first 48 terms \(= (8)(0) = 0\)
All we need to do now is add \(t_ {49} \) and \(t_ {50} \)

We can follow the pattern to see that \(t_ {49} = 1\) and \(t_ {50} = 1\), which means the sum of the first 50 terms = 2

Answer: E
avatar
Intern
Intern
Joined: 13 Oct 2021
Posts: 3
Own Kudos [?]: 2 [0]
Given Kudos: 4
Send PM
Re: The sequence of numbers t_1, t_2, [#permalink]
Since the question says n>2, shouldn't we be checking from t3 to t52?
Retired Moderator
Joined: 02 Dec 2020
Posts: 1833
Own Kudos [?]: 2146 [1]
Given Kudos: 140
GRE 1: Q168 V157

GRE 2: Q167 V161
Send PM
Re: The sequence of numbers t_1, t_2, [#permalink]
1
The batch of certain terms gets repeated in the series hence we don't need to calculate till \(t_{52}\).

pgirikishore wrote:
Since the question says n>2, shouldn't we be checking from t3 to t52?
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12188 [1]
Given Kudos: 136
Send PM
Re: The sequence of numbers t_1, t_2, [#permalink]
1
pgirikishore wrote:
Since the question says n>2, shouldn't we be checking from t3 to t52?


t1 and t2 are still part of the sequence.
So they will be included in the sum of terms from t1 to t50
Prep Club for GRE Bot
Re: The sequence of numbers t_1, t_2, [#permalink]
Moderators:
GRE Instructor
78 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne