In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn

Question

In the arithmetic sequence  t_1 ,  t_2 ,  t_3 , ...,  t_n ,  t_1=23  and  t_n= t_{n-1} - 3  for each n > 1. What is the value of n when  t_n = -4 ?

A. -1
B. 7
C. 10
D. 14
E. 20

Bunuel · Accepted Answer

t_n=t_{n-1}-3  means that each term is 3 less than the previous term. Now, the difference between  t_1=23  and  t_n=-4  is  23-(-4)=27 , so we moved  \frac{27}{3}=9  terms from  t_1 , so from  t_1  to  t_{10} .

Answer: C.

LalaB · Answer

tn= tn-1 - 3 means that d=-3

tn=t1 +d(n-1)
-4=23-3(n-1)
-30=-3n
n=10

liko21 · Answer

well.....t 2 =t 1 -3 =23-3=20 t 3 =t 2 -3=20-3=17 So every time we n increases tn decreases by 3. Since t 1 =23 we have 23-3=20-3=17-3=14-3=11-3=8-3=5-3=2-3=-1-3=-4!VOILA So n=10 ten times substructing 3 from 23 to reach -4. clear :?:

PareshGmat · Answer

23... 20.... 17... 14... 11.... 8... 5... 2.... -1....   -4

-4 is the 10th term

Answer = 10

pacifist85 · Answer

I also did the same as Paresh, but like this:

We know that t1 = 23
So, using the given formula we have: 
t1=(t1-1) -3 =23
t0 - 3 = 23
t0= 26

The sam way we find that t2= 20

It seems that the sequence goes like this:
t0 = 26
t1 = 23
t2 = 20
t3 = 17
t4 = 14
t5 = 11
t6 = 8
t7 = 5
t8 = 2
t9 = -1
t10 = -4

So, our  ANS is C .

However, I did do it wrong because, by the way I saw it writen, I though that the whole formula equaled to 23 (t1, t2, t3, ..., tn, t1=23). I didn't see any relationship as to why this is 23 (it is an addition, is it a multiplication?). So, then I thought that what was meant is that this sequence is doing a circle, going from t1 to t1 again, and there are 23 numbers in the sequence. So, I though we needed to find tn.

Hopefully the gmat would show in a more clear way that t1=23 and not the whole sequence..

prajaktt · Answer

t1=23
t2=t1-3=20
t3=t2-3=17 and so on...
Here is when we need to consider the formula for AP as we know the   common difference is -3

tn=t1 + d(n-1)

given, tn=-4
-4=23 + (-3) (n-10) >>   n=10  
 
Ans : C

Sumitj2016 · Answer

Its a normal arithmetic Progression Question , whose 1st term is 23 and common difference is -3

Tn = a+ (n-1)d

-4 = 23 +(n-1)(-3)

n = 10 .

JeffTargetTestPrep · Answer

In the given sequence, since we are given the first term, we can use that value to find the second term, and once we know the second term, we can use that value to find the third term, and so on.
 
t_1 = 23
 
t_2 = t_1 – 3 = 23 – 3 = 20
 
t_3 = t_2 – 3 = 20 – 3 = 17
 
t_4 = t_3 – 3 = 17 – 3 = 14
 
t_5 = t_4 – 3 = 14 – 3 = 11
 
t_6 = t_5 – 3 = 11 – 3 = 8
 
t_7 = t_6 – 3 = 8 – 3 = 5
 
t_8 = t_7 – 3 = 5 – 3 = 2
 
t_9 = t_8 – 3 = 2 – 3 = -1
 
t_10 = t_9 – 3 = -1 – 3 = -4
 
So n = 10.
 
Alternative Solution:
 
Notice that starting from the second term, each term is 3 less than the previous term, which makes the sequence an arithmetic sequence. In an arithmetic sequence, the nth term, a_n, can be found by using the formula a_n = a_1 + d(n – 1) in which a_1 is the first term and d is the common difference.
 
Since we are given t_n, we can modify the formula to t_n = t_1 + d(n – 1) in which t_1 = 23 and d = -3. So we have:
 
t_n = t_1 + d(n – 1)
 
-4 = 23 + (-3)(n – 1)
 
-27 = -3(n – 1)
 
9 = n – 1
 
10 = n
 
Answer: C

mcelroytutoring · Answer

Attached is a visual that should help.

hmazariegos · Answer

Here is how I did it:

t1 = 23 and tn-1 = -3; therefore for every t you need to subtract 3

lets begin:

t1----> 23-3 = 20
t2----> 20-3 = 17
t3----> 17-3 = 14

when tn = 4...now subtract 4 from the 14

tn----> 14-4 = 10

Answer is C

EMPOWERgmatRichC · Answer

Hi All,

Questions that use "sequence notation" are relatively rare on Test Day (you'll probably see just 1), but the math behind the sequence is usually some fairly simple arithmetic (add, subtract, multiply, divide).

Here, we're given the first term in the sequence (23) and we're told that each term thereafter is 3 LESS than the preceding term. Once you understand how the sequence "works", in many cases, it's really easy to just "map out" the sequence. We're asked which term in the sequence equals -4.....

1st = 23 
2nd = 20 
3rd = 17 
4th = 14 
5th = 11 
6th = 8 
7th = 5 
8th = 2 
9th = -1 
10th = -4

Final Answer:  C

GMAT assassins aren't born, they're made, 
Rich

Mangalshubham · Answer

a sequence of numbers contains terms t1, t2, t3,......... , tn, where every term is equal to the sum of its two preceding terms. t5 =18 and t8 = 76 what is the value of t9

Answer this

EMPOWERgmatRichC · Answer

Hi Mangalshubham,

In the future, when posting questions, you should post each in its own unique thread AND you should make sure to post the ENTIRE prompt (with the 5 answer choices and the correct answer - hidden behind a "spoiler" tag).

The prompt you've submitted is a sequence question that you can use to create the following equations. We're told that each term is equal to the SUM of the TWO terms that immediately precede it...

5th term = 18
6th term = X
7th term = 18+X
8th term = 76 = (X + 18 + X)

76 = 2X + 18
58 = 2X
29 = X

Thus, we have...

5th term = 18
6th term = 29
7th term = 47
8th term = 76 
9th term = ?

Final Answer:  47+76 = 123

GMAT assassins aren't born, they're made,
Rich

EMPOWERgmatRichC · Answer

Hi All,

Questions that use "sequence notation" are relatively rare on Test Day (you'll probably see just 1), but the math behind the sequence is usually some fairly simple arithmetic (add, subtract, multiply, divide).

Here, we're given the first term in the sequence (23) and we're told that each term thereafter is 3 LESS than the preceding term. Once you understand how the sequence "works", in many cases, it's really easy to just "map out" the sequence. We're asked which term in the sequence equals -4.....

1st = 23 
2nd = 20 
3rd = 17 
4th = 14 
5th = 11 
6th = 8 
7th = 5 
8th = 2 
9th = -1 
10th = -4

Final Answer:  C

GMAT assassins aren't born, they're made, 
Rich

CrushTheQuant · Answer

This YouTube video breaks down how to solve this particular question:

https://www.youtube.com/watch?v=--anIA9 ... t1&index=7

The fundamentals of handling any sequence problem are to first jot down the following:

t1 , t2 , t3, t4... t(n-1)... t(n)

(FYI - you would be writing the numbers and the "(n-1)" and the "n" as SUBSCRIPTS (i.e. we're not multiplying here...)

The next step is to begin writing a formula right underneath t(n). Simply write t(n) =

Third step to to fill out that formula. It may be that t(n) is related to the term than came before; in this problem, for example, t(n) = t(n-1) - 3

In another problem, t(n) may be related to "n" itself, for example t(n) = n^2 +5

(FYI - on rare occasion, a problem have a more bizarre rule, like "t(n) = 2 when n is odd, and t(n) = 3 when n is even")

Basshead · Answer

We're told:  t1 = 23

From that we can derive the following values:

t2 = 23 - 3 = 20 
 t3 = 20 - 3 = 17 
 t4 = 14 
 t5 = 11 
 t6 = 8 
 t10 = -4

Answer is C.

CrackverbalGMAT · Answer

nth term of an AP = a + (n-1)d

where a= first term and d = common difference

-4 = 23 + (n-1)-3

-27 = -3n +4

-30 = -3n
n = 10

Option C is the answer.

Thanks,
Clifin J Francis,
GMAT SME

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In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn

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In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn

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