GRE Math : Arithmetic Sequences

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #11 : Sequences

The sequence  is defined by:

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

For this problem, you definitely do not want to "count upwards" to the full value of the sequence.  Therefore, the best approach is to consider the general pattern that arises from the general definition:

This means that for every element in the list, each one is  less than the one preceding it.  For instance:

Now, notice that the first element is:

The second is:

The third could be represented as:

And so forth...

Now, notice that for the third element, there are only two instances of .  We could rewrite our sequence:

This value will always "lag behind" by one.  Therefore, for the th element, you will have:

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