SSAT Upper Level Math : How to find the nth term of an arithmetic sequence

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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Example Question #41 : Sequences And Series

The lengths of the sides of ten squares form an arithmetic sequence. One side of the smallest square measures eight inches; one side of the second-smallest square measures one foot. 

Give the area of the largest square.

Possible Answers:

784 square inches

484 square inches

1,936 square inches

2,304 square inches

576 square inches

Correct answer:

1,936 square inches

Explanation:

Let  be the lengths of the sides of the squares in inches.  and , so their common difference is

The arithmetic sequence formula is 

The length of a side of the largest square - square 10 - can be found by substituting :

 

The largest square has sides of length 44 inches, so its area is the square of this, or  square inches.

Example Question #42 : Sequences And Series

An arithmetic sequence begins as follows:

Give the thirty-second term of this sequence.

Possible Answers:

Correct answer:

Explanation:

The th term of an arithmetic sequence with initial term  and common difference  is defined by the equation

The initial term in the given sequence is

;

the common difference is

;

We are seeking term .

This term is  

 

Example Question #43 : Sequences And Series

An arithmetic sequence begins as follows:

Give the thirty-third term of this sequence.

Possible Answers:

The correct answer is not given among the other four responses.

Correct answer:

The correct answer is not given among the other four responses.

Explanation:

The th term of an arithmetic sequence with initial term  and common difference  is defined by the equation

.

The initial term in the given sequence is

;

the common difference is

.

We are seeking term .

Therefore,

,

which is not among the choices.

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