SAT Math : How to find the nth term of an arithmetic sequence

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #11 : How To Find The Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows: 14, 27, 40...

What is the first four-digit integer in the sequence?

Possible Answers:

Correct answer:

Explanation:

Given the first two terms  and , the common difference  is equal to the difference:

Setting :

The th term of an arithmetic sequence  can be found by way of the formula

Since we are looking for the first four-digit whole number - equivalently, the first number greater than or equal to 1,000:

Setting  and  and solving for :

Therefore, the 77th term, or , is the first element in the sequence greater than 1,000. Substituting , and   in the rule and evaluating:

,

the correct choice.

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