Question

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

an = 65n + 80

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the first five terms of the sequence, we can substitute the values for n starting with n = 1 and calculate each term.

For n = 1:
a1 = 65(1) + 80 = 65 + 80 = 145

For n = 2:
a2 = 65(2) + 80 = 130 + 80 = 210

For n = 3:
a3 = 65(3) + 80 = 195 + 80 = 275

For n = 4:
a4 = 65(4) + 80 = 260 + 80 = 340

For n = 5:
a5 = 65(5) + 80 = 325 + 80 = 405

Therefore, the first five terms of the sequence defined by an = 65n + 80 are:
145, 210, 275, 340, 405.

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 = 10(10)n

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the first four terms of the sequence, we can substitute the values for n starting with n = 1 and calculate each term.

For n = 1:
a1 = 10(10)(1) = 10(10) = 100

For n = 2:
a2 = 10(10)(2) = 10(20) = 200

For n = 3:
a3 = 10(10)(3) = 10(30) = 300

For n = 4:
a4 = 10(10)(4) = 10(40) = 400

Therefore, the first four terms of the sequence defined by an = 10(10)n are:
100, 200, 300, 400.

Answer 4

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 = 7n2 − n − 1

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the first four terms of the sequence, we can substitute the values for n starting with n = 1 and calculate each term.

For n = 1:
a1 = 7(1)^2 − 1(1) − 1 = 7 − 1 − 1 = 5

For n = 2:
a2 = 7(2)^2 − 2(2) − 1 = 28 − 4 − 1 = 23

For n = 3:
a3 = 7(3)^2 − 3(3) − 1 = 63 − 9 − 1 = 53

For n = 4:
a4 = 7(4)^2 − 4(4) − 1 = 112 − 16 − 1 = 95

Therefore, the first four terms of the sequence defined by an = 7n^2 − n − 1 are:
5, 23, 53, 95.