The nth term of an arithmetic sequence

Question 1

Find the nth term of this sequence:

3, 7, 11, 15, …

Answer 1

4n - 1

(4 is the common difference; -1 is first term subtract common difference)

Question 2

Find the nth term of this sequence:

4, 10, 16, 22, …

Answer 2

6n - 2

(6 is the common difference; -2 is first term subtract common difference)

Question 3

Find the nth term of this sequence:

5, 8, 11, 14, 17, …

Answer 3

3n + 2

(3 is the common difference; +2 is first term subtract common difference)

Question 4

Find the nth term of this sequence:

16, 23, 30, 37 …

Answer 4

7n + 9

(7 is the common difference; +9 is first term subtract common difference)

Question 5

Find the nth term of this sequence:

-7, -3, 1, 5, …

Answer 5

4n - 11

(4 is the common difference; -11 is first term subtract common difference)

Question 6

Find the nth term of this sequence:

-2, 4, 10, 16, …

Answer 6

6n - 8

(6 is the common difference; -8 is first term subtract common difference)

Question 7

Find the nth term of this sequence:

21, 19, 17, 15, …

Answer 7

-2n + 23 or 23 - 2n

(-2 is the common difference; +23 is first term subtract common difference)

Question 8

Find the nth term of this sequence:

32, 27, 22, 17, …

Answer 8

-5n + 37 or 37 - 5n

(-5 is the common difference; 37 is first term subtract common difference)

Question 9

The nth term of 8, 11, 14, 17, … is 3n + 5.

Is 128 a term in this sequence? Explain.

Answer 9

Yes, 128 is a term in the sequence

because 3 x 41 + 5 = 128, so it is the 41st term. (3n + 5 = 128 gives 3n = 123 gives n = 41)

Question 10

The nth term of 2, 8, 14, 20, … is 6n - 4.

Is 118 a term in this sequence? Explain.

Answer 10

No, 118 is not a term in the sequence

because 6 x 20 - 4 = 116 and 6 x 21 - 4 = 122. (6n - 4 = 118 gives 6n = 122 gives n = 20.333… , but n must be a whole number)

Question 11

The nth term of 1, 5, 9, 13, … is 4n - 3.

Is 197 a term in this sequence? Explain.

Answer 11

Yes, 197 is a term in the sequence

because 4 x 50 - 3 = 197, so it is the 50th term. (4n - 3 = 197 gives 4n = 200 gives n = 50)

Question 12

The nth term of 8, 15, 22, 29, … is 7n + 1.

Is 144 a term in this sequence? Explain

Answer 12

No, 144 is not a term in the sequence

because 7 x 20 + 1 = 141 and 7 x 21 = 1 = 148. (7n + 1 = 144 gives 7n = 143 gives n = 20.428… , but n must be a whole number)