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In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = -4?

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

I struggled badly on this question? Can you please help?

\(t_n=t_{n-1}-3\) 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 \(t_{10}\).

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

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03 Feb 2015, 00:44

2

This post received KUDOS

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..

In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn= tn-1 - 3 for each n > 1. What is the value of n when tn = -4?

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

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
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Re: In the arithmetic sequence t1, t2, t3, ..., tn, t1=23 and tn [#permalink]

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01 Dec 2017, 19:53

i have one doubt in the question.Why cant we use the AP formula for the nth term to calculate the number if terms.When i did , i get n to be 8. Why is that method incorrect?

i have one doubt in the question.Why cant we use the AP formula for the nth term to calculate the number if terms.When i did , i get n to be 8. Why is that method incorrect?