Question

Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.

an = 3(3)n

Answer 1

Find the first three terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.

an = –8n − 4

Answer 2

Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.

an = 2(4)n

Answer 3

To find the first four terms of the sequence defined by an = 3(3)n, we substitute the values of n from 1 to 4 into the formula:

When n = 1:
a1 = 3(3)^1 = 3(3) = 9

When n = 2:
a2 = 3(3)^2 = 3(9) = 27

When n = 3:
a3 = 3(3)^3 = 3(27) = 81

When n = 4:
a4 = 3(3)^4 = 3(81) = 243

Therefore, the first four terms of the sequence are 9, 27, 81, and 243.

Answer 4

To find the first three terms of the sequence defined by an = –8n – 4, we substitute the values of n from 1 to 3 into the formula:

When n = 1:
a1 = –8(1) – 4 = –8 – 4 = –12

When n = 2:
a2 = –8(2) – 4 = –16 – 4 = –20

When n = 3:
a3 = –8(3) – 4 = –24 – 4 = –28

Therefore, the first three terms of the sequence are –12, –20, and –28.

Answer 5

To find the first four terms of the sequence defined by an = 2(4)n, we substitute the values of n from 1 to 4 into the formula:

When n = 1:
a1 = 2(4)^1 = 2(4) = 8

When n = 2:
a2 = 2(4)^2 = 2(16) = 32

When n = 3:
a3 = 2(4)^3 = 2(64) = 128

When n = 4:
a4 = 2(4)^4 = 2(256) = 512

Therefore, the first four terms of the sequence are 8, 32, 128, and 512.