SSAT Upper Level Quantitative › How to find the nth term of an arithmetic sequence
An arithmetic sequence begins as follows:
Which of the following is the first term greater than 100?
The forty-first term
The forty-second term
The forty-third term
The forty-fourth term
The fortieth term
The common difference of the sequence is
so the th term of the sequence is
To find out the minimum value for which , set up this inequality:
The forty-first term is the correct response.
An arithmetic sequence begins as follows:
Which of the following is the first term greater than 100?
The forty-eighth term
The forty-ninth term
The fiftieth term
The forty-seventh term
The fifty-first term
The common difference of the sequence is
so the th term of the sequence is
To find out the minimum value for which , set up this inequality:
The correct response is the forty-eighth term.
An arithmetic sequence begins as follows:
Which of the following terms is the first positive term in the sequence?
The fortieth term
The thirty-ninth term
The thirty-eighth term
The thirty-seventh term
The sequence has no positive terms.
The common difference of the sequence is
,
so the th term of the sequence is
To find out the minimum value for which , set up this inequality:
The first positive term is the fortieth term.
The first two terms of an arithmetic sequence are 1,000 and 997, in that order. What is the seventieth term?
The first term is .
The common difference is
.
The seventieth term is
.
An arithmetic sequence begins as follows:
Give the thirty-third term of this sequence.
The correct answer is not given among the other four responses.
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.
An arithmetic sequence begins as follows:
Give the thirty-second term of this sequence.
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
An arithmetic sequence begins as follows:
Which of the following terms is the first negative term in the sequence?
The one hundred thirteenth term
The one hundred twelfth term
The one hundred eleventh term
The one hundred tenth term
The one hundred fourteenth term
The common difference of the sequence is
so the th term of the sequence is
To find out the minimum value for which , set up this inequality:
The first negative term is the one hundred thirteenth term.
The eleventh and thirteenth terms of an arithmetic sequence are, respectively, 11 and 14. Give its first term.
The th term of an arithmetic sequence with initial term
and common difference
is defined by the equation
Since the eleventh and thirteenth terms are two terms apart, the common difference can be found as follows:
Now, we can set in the sequence equation to find
:
The first two terms of an arithmetic sequence are 4 and 9, in that order. Give the one-hundredth term of that sequence.
The first term is ; the common difference is
.
The hundredth term is
.
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.
1,936 square inches
484 square inches
2,304 square inches
576 square inches
784 square inches
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.