Problem Solving

Can someone help explain this problem?

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?

Answers:

-1

7

10

14

20

Correct answer is 10.

melanie.espeland wrote:Can someone help explain this problem?

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?

Answers:

-1

7

10

14

20

Correct answer is 10.

An arithmetic sequence is a simple sequence in which each term is an equal amount different, d, from the previous term.

In the arithmetic sequence 2 4 6 8 10..., each term is just 2 greater than the term before it. 2 would be t1, or alternatively t0, and each of the other terms is t2, t3, t4...

In these cases it can be pretty easy to find the value of a term.

For a term tn, tn = t1 + (n - 1)d. So in the case of 2 4 6 8 10..., the sixth term, t6, is 2 + (6 - 1)2 = 12

One can also work it backwards to find n, which is the question in this case.

Translated the question is basically, How many times do we need to add the difference, -3, to 23 to get to -4?

t1 = 23 and d = -3

So we have -4 = 23 + (n - 1)-3

-27 = (n - 1)-3

9 = n - 1

n = 10

Do you need to memorize the above formula? Not really. If you see a sequence on the test, it is likely that this formula will not fit that sequence anyway.

What you do need is to understand sequence notation and get the general idea of how sequences work so that you can apply that creatively when you see a sequence question on the test.

Thank you both for feedback. As an fyi, I just took a GMAT official practice exam and there were two sequence problems (this being one of them).

Sincerely,

Melanie

Alternate approach:

T(n) = T(n) - 3.

According to the formula above, each term is 3 less than the preceding term.
The result is an EVENLY SPACED SET.

To count the number of integers in an evenly spaced set, use the following formula:
(biggest - smallest)/interval + 1.
The interval is the distance between successive terms.

Here, the interval is 3, since each term is 3 less than the preceding term.
Since the biggest term = 23 and the smallest term = -4, we get:
Number of terms = (biggest - smallest)/interval + 1 = [23 - (-4)]/3 + 1 = 10.

The correct answer is C.