## In the arithmetic sequence t1, t2, t3,......., t(n)

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gphil

### In the arithmetic sequence t1, t2, t3,......., t(n)

I would greatly appreciate help with the following problem.
Thanks!

In the arithmetic sequence t1, t2, t3,......., t(n), t1=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 - correct
D) 14
E) 20
Guest

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

t(n)=t(n-1)-3 states that the next term is 3 less than the previous term.

Since we know term 1 = 23, t2 = 20 and so on.

it's probably faster to find each term than to make a math equation:

t1=23
t2=20
t3=17
t4=14
t5=11 (we can see we're getting closer to -4)
t6=8
t7=5
t8=2
t9=-1
t10=-4 - therefore D is correct.

A) -1
B) 7
C) 10 - correct
D) 14
E) 20
Guest

I meant C is correct in the above message. (Admin can you please correct it).
gphil

Thanks a lot for explanation!

If I get a similar question on the exam and the values will be too far apart, which method would you suggest to use?

Thanks!
Amit

In the case where the numbers are farther apart (notice the use of farther vs. further from S.C. studying) I would make an equation to solve.

For example:

t1=23
t2=20
t3=17
...
I know that we subract 3 each time we get the new term, so we need -3n somewhere.
We can say t(n) = 26 - 3n. I used 26 because if I plug in n=1, it works for the first equation.

Using the equation and t(n)=-4,:

-4 = 26 - 3n
3n = 30
n = 10

This may look shorter, but during the GMAT I would suggest to just count downwards because you save the risk of creating an incorrect equation and/or simplifying your equation incorrectly.

Cheers!
gphil

Thanks a lot!
Course Students

Posts: 5
Joined: Sat Jan 23, 2016 3:28 am

### Re:

Amit wrote:In the case where the numbers are farther apart (notice the use of farther vs. further from S.C. studying) I would make an equation to solve.

For example:

t1=23
t2=20
t3=17
...
I know that we subract 3 each time we get the new term, so we need -3n somewhere.
We can say t(n) = 26 - 3n. I used 26 because if I plug in n=1, it works for the first equation.

Using the equation and t(n)=-4,:

-4 = 26 - 3n
3n = 30
n = 10

This may look shorter, but during the GMAT I would suggest to just count downwards because you save the risk of creating an incorrect equation and/or simplifying your equation incorrectly.

Cheers!

How did you figure out the "-3n"? and why the "26"? Following this method and given this problem, I would've started with the "23" which would've lead to n=9, which is not an answer.

Just trying to learn how to solve this type of problem...

Thanks!
RonPurewal
Students

Posts: 19747
Joined: Tue Aug 14, 2007 8:23 am

### Re: Re:

EstanisladoM601 wrote:How did you figure out the "-3n"? and why the "26"?

(you're replying to a post that's almost 10 years old, so... it's very unlikely that you'll get an answer from the original poster)

this sequence "steps down" by 3 every time, so, that's where the "–3n" comes from.
(the value of the sequence goes down by 3 every time "n" increases by 1. if you were to graph this, it would give a line whose slope is –3/1 = –3.)

you can figure out the 26 by just throwing a pair in there -- like (1, 23) or (2, 20) or any other pair.
if you use (1, 23), then it's
MYSTERY NUMBER – 3(1) = 23
so
MYSTERY NUMBER = 26
Course Students

Posts: 5
Joined: Sat Jan 23, 2016 3:28 am

### Re: In the arithmetic sequence t1, t2, t3,......., t(n)

Thank you Ron.
RonPurewal
Students

Posts: 19747
Joined: Tue Aug 14, 2007 8:23 am

you're welcome.