GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Jul 2020, 05:03 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # In a sequence of numbers t1, t2, t3, ... the difference of any two suc

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 64996
In a sequence of numbers t1, t2, t3, ... the difference of any two suc  [#permalink]

### Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 78% (01:54) correct 22% (02:14) wrong based on 18 sessions

### HideShow timer Statistics

In a sequence of numbers $$t_1$$, $$t_2$$, $$t_3$$, ... the difference of any two successive terms is a constant. If $$|t_8| = |t_{16}|$$ and $$t_3 ≠ t_7$$, what is the sum of the first 23 terms of the sequence?

A. -10
B. -4
C. 0
D. 4
E. 10

Are You Up For the Challenge: 700 Level Questions

_________________
DS Forum Moderator V
Joined: 19 Oct 2018
Posts: 1980
Location: India
Re: In a sequence of numbers t1, t2, t3, ... the difference of any two suc  [#permalink]

### Show Tags

1
nth term of the sequence = a+(n-1)d

a= first term
d= the difference of any two successive terms

$$t_3 ≠ t_7$$

$$a+2d ≠ a+6d$$

d≠0

$$|t_8| = |t_{16}|$$

$$|a+7d| = |a+15d|$$

$$Case 1-$$ a+7d= a+15d

We get d=0 (not possible)

Reject this case

Case 2- a+7d= -(a+15d)

2a+22d=0 or a+11d =0

Sum of first 23 terms = Mean of 23 terms * 23

Mean of 23 terms = 12th term of the sequence = a+11d

Sum of first 23 terms = (a+11d) * 23 = 0

Bunuel wrote:
In a sequence of numbers $$t_1$$, $$t_2$$, $$t_3$$, ... the difference of any two successive terms is a constant. If $$|t_8| = |t_{16}|$$ and $$t_3 ≠ t_7$$, what is the sum of the first 23 terms of the sequence?

A. -10
B. -4
C. 0
D. 4
E. 10

Are You Up For the Challenge: 700 Level Questions
Senior Manager  G
Joined: 14 Oct 2019
Posts: 406
Location: India
GPA: 4
WE: Engineering (Energy and Utilities)
Re: In a sequence of numbers t1, t2, t3, ... the difference of any two suc  [#permalink]

### Show Tags

In a sequence of numbers t1t1, t2t2, t3t3, ... the difference of any two successive terms is a constant. If |t8|=|t16| and t3≠t7, what is the sum of the first 23 terms of the sequence?

Tn = a + (n - 1) d, where Tn = nth term and a = first term. Here d = common difference = Tn - Tn-1.
Sn =(n/2)[2a + (n- 1)d]

given,|t8|=|t16I
or,|a+7d|=|a+15d|
case I : a+7d= a+15d
or, d=0 which is not possible because if common difference is zero each term is equal which invalidates t3≠t7 .

so, case II : a+7d= -(a+15d)
or, 2a + 22d = 0

now, the sum of the first 23 terms of the sequence
=(23/2)[2a + (23- 1)d]
=23/2[2a + 22d ]
=0

GMAT Tutor S
Joined: 16 Sep 2014
Posts: 517
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Re: In a sequence of numbers t1, t2, t3, ... the difference of any two suc  [#permalink]

### Show Tags

Bunuel wrote:
In a sequence of numbers $$t_1$$, $$t_2$$, $$t_3$$, ... the difference of any two successive terms is a constant. If $$|t_8| = |t_{16}|$$ and $$t_3 ≠ t_7$$, what is the sum of the first 23 terms of the sequence?

A. -10
B. -4
C. 0
D. 4
E. 10

Are You Up For the Challenge: 700 Level Questions

The scenario here is either $$t_8 = -t_{16}$$, or all terms have a difference of 0. Since $$t_3 ≠ t_7$$ we clearly cannot have a difference of 0, thus we can conclude $$t_8 = -t_{16}$$.

Note there are no actual numbers present in this question, an educated guess would be to choose C since we don't have any numbers to conclude an answer like 4 or 10.

In fact we do have $$t_9 = -t_{15}$$, $$t_{10} = -t_{14}$$, and $$t_{11} = -t_{13}$$, so we must have $$t_{12} = 0$$. Any sum centered around $$t_{12}$$ would also be equivalent to zero, the terms 1 to 23 have a center of 12 so that sum is indeed equal to 0.

Ans: C
_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. Feel free to reach out!
Intern  B
Joined: 28 Mar 2018
Posts: 44
In a sequence of numbers t1, t2, t3, ... the difference of any two suc  [#permalink]

### Show Tags

Bunuel wrote:
In a sequence of numbers $$t_1$$, $$t_2$$, $$t_3$$, ... the difference of any two successive terms is a constant. If $$|t_8| = |t_{16}|$$ and $$t_3 ≠ t_7$$, what is the sum of the first 23 terms of the sequence?

A. -10
B. -4
C. 0
D. 4
E. 10

Are You Up For the Challenge: 700 Level Questions

If |t8|=|t16|, then logically one of them is negative and other one is positive, with equal value
In such case, the middle value between t8 and t16, which is t12, must be 0 (this middle value basically indicates the transition from negative to positive or vice versa)

Now, S23 = (23/2) x (2a + 22d) = 23(a + 11d) = 23 x t12 = 0

Posted from my mobile device In a sequence of numbers t1, t2, t3, ... the difference of any two suc   [#permalink] 16 May 2020, 13:17

# In a sequence of numbers t1, t2, t3, ... the difference of any two suc   