GRE Math Help » Arithmetic » Integers » Sequences » Arithmetic Sequences » Other Arithmetic Sequences » How to find the answer to an arithmetic sequence

What is the sum of the odd integers

?

Explanation:

Do NOT try to add all of these. It is key that you notice the pattern. Begin by looking at the first and the last elements: 1 and 99. They add up to lớn 100. Now, consider 3 và 97. Just as 1 + 99 = 100, 3 + 97 = 100. This holds true for the entire list. Therefore, it is crucial that we find the number of such pairings.

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1, 3, 5, 7, and 9 are paired with 99, 97, 95, 93, và 91, respectively. Therefore, for each 10s digit, there are 5 pairings, or a total of 500. Khổng lồ get all the way through our numbers, you will have lớn repeat this process for the 10s, 20s, 30s, và 40s (all the way lớn 49 + 51 = 100).

Therefore, there are 500 (per pairing) * 5 pairings = 2500.

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### Example Question #2 : How khổng lồ Find The Answer to An Arithmetic Sequence

A sequence is defined by the following formula:

What is the 4th element of this sequence?

Explanation:

With series, you can always "walk through" the values lớn find your answer. Based on our equation, we can rewrite

as :

You then continue for the third & the fourth element:

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### Example Question #1 : Sequences

What is the sum of the 40th và the 70th elements of the series defined as:

Explanation:

When you are asked to find elements in a series that are far into its iteration, you need khổng lồ find the pattern. You absolutely cannot waste your time trying to calculate all of the values between

and
. Notice that for every element after the first one, you subtract
. Thus, for the second element you have:

For the third, you have:

Therefore, for the 40th và 70th elements, you will have:

The sum of these two elements is:

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