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

[gphil]

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!

[EstanisladoM601]

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]

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

[EstanisladoM601]

Thank you Ron.

[RonPurewal]

you're welcome.