The sequence -7, -14,  – 21, – 28, … looks like 1, 2, 3, 4, … except each term is multiplied by – 7. So, the expression that describes the sequence is –7n, where n represents the position of a term in the sequence. Check the first four terms:

To find the 1^st term, plug in n = 1.

-7n =  – 7(1) = – 7

To find the 2nd term, plug in n = 2.

–7n = – 7(2) = – 14

To find the 3rd term, plug in n = 3.

– 7n = – 7(3) = – 21

To find the 4th term, plug in n = 4.

– 7n = – 7(4) = – 28

The sequence – 7, – 14, – 21, – 28, … is described by the expression – 7n.

The sequence -7, – 6, – 5, – 4, … looks like 1, 2, 3, 4, … except each term is 8 smaller. So, the expression that describes the sequence is n − 8. Check the first four terms:

To find the 1st term, plug in n = 1.

n − 8 = 1 − 8 = –7

To find the 2nd term, plug in n = 2.

n − 8 = 2 − 8 = –6

To find the 3rd term, plug in n = 3.

n − 8 = 3 − 8 = – 5

To find the 4th term, plug in n = 4.

n − 8 = 4 − 8 = – 4

The sequence –7, – 6, – 5, – 4, … is described by the expression n − 8.

The sequence 4, 8, 12, 16, … looks like 1, 2, 3, 4, … except each term is 4 times as large. So, the expression that describes the sequence is 4n, where n represents the position of a term in the sequence. Check the first four terms:

To find the 1st term, plug in n = 1.

4n = 4(1) = 4

To find the 2nd term, plug in n = 2.

4n = 4(2) = 8

To find the 3rd term, plug in n = 3.

4n = 4(3) = 12

To find the 4th term, plug in n = 4.

4n = 4(4) = 16

The sequence 4, 8, 12, 16, … is described by the expression 4n.