Question

Check the statements that are true.

A. An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers.
B. A geometric sequence is a linear function whose domain is restricted to the set of non-negative integers.
C. An arithmetic sequence is an exponential function whose domain is restricted to the set of non-negative integers.
D. A geometric sequence is an exponential function whose domain is restricted to the set of non-negative integers.

Answer 1

An arithmetic sequence is a linear function and a geometric sequence is an exponential function.

Step-by-step explanation:

The correct statements are A and D.

A. An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers. This means that the sequence follows a constant pattern of adding or subtracting the same number to each term to get the next term. Example: 2, 4, 6, 8, 10

D. A geometric sequence is an exponential function whose domain is restricted to the set of non-negative integers. This means that the sequence follows a constant pattern of multiplying or dividing the same number to each term to get the next term. Example: 2, 4, 8, 16, 32

Answer 2

A and D.

Step-by-step explanation:

A sequence is a set of the objects or numbers in a specific order. It is a function whose domain is a set of natural numbers or non-negative integers i.e. {1, 2, 3,..}

(A)

"An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers."

The general form an arithmetic sequence is:

`a_(n)=a_(1)+(n-1)d`

The function is linear. The sequence consists of either numbers that are increasing or decreasing based on the value of d, the common difference.

So, the statement provided is True.

(D)

"A geometric sequence is an exponential function whose domain is restricted to the set of non-negative integers."

The general form an geometric sequence is:

`a_(n)=a_(1)\cdot r^(n-1)`

The function is exponential. The sequence consists of either numbers that are exponentially increasing or decreasing by the factor r, the common ratio.

So, the statement provided is True.