Question

A sequence is defined below.Q1 = 1An+1 = -an for all n ENWhich of the following statements is true?O A. The rule an = (-1)"+1 represents a function with domain D = { - 1,1}.O B. The map nan represents a function with domain N, the set of natural numbers.O C. The notations (an)nen and (an+2)nen represent two different sequences.D. The notation (an+1)nen represents a finite sequence with first term -1.

Answer 1

Write out the sequence as defined below

`\begin{gathered} Q_1\text{ = 1} \\ A_{n+1\text{ = }}\text{ -an for all nEN} \\ \end{gathered}`

Option A

The rule an = (-1)"+1 represents a function with domain D = { - 1,1} (True)

Reason

`\begin{gathered} A_1=-1^(1+1) \\ 1=-1^2 \\ 1\text{ = 1} \end{gathered}`

Option B

The map nan represents a function with domain N, the set of natural numbers (True)

Reason : For all set of natural numbers the map nan represents a function with domain N

Option C

The notations (an)nen and (an+2)nen represent two different sequences (False)

Option D

The notation (an+1)nen represents a finite sequence with first term -1 (False)

Hence Option A & B are true statements