Question

An arithmetic sequence is shown.

​​​288, 209, 130, 51,−28, ...

a. The claim about linear functions is correct, and the specific function is also correct.

b. The claim about linear functions is correct, but the specific function uses an incorrect initial value.

c. The claim about linear functions is incorrect because arithmetic sequences are not related at all to linear functions.

d. The claim about linear functions is incorrect because arithmetic sequences can only be expressed recursively with linear functions.

Answer 1

The claim about linear functions is correct, and the specific function is also correct. Option A is correct

Given the sequence of numbers 288, 209, 130, 51,−28, ..., the nth term of the sequence is expressed as:

Tn = a + (n- 1)d

a is the first term

d is the common difference

d = 209 - 288 = 130 - 209 = -79

Get the linear function

Tn = 288 + (n - 1)(-79)

Tn =  288 -79n + 79

Tn  = -79n + 367

This shows that the claim about linear functions is correct, and the specific function is also correct.

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