Question

Which sequence has the given function notation f(n)=n2
when defined explicitly?(1 point)
Responses

an=2, 4, 6, 8, 10 . . .
a subscript n baseline equals 2 comma 4 comma 6 comma 8 comma 10 dot dot dot

an=1, 1, 1, 1, 1 . . .
a subscript n baseline equals 1 comma 1 comma 1 comma 1 comma 1 dot dot dot

an=1, 4, 9, 16, 25 . . .
a subscript n baseline equals 1 comma 4 comma 9 comma 16 comma 25 dot dot dot

an=1
; an=(an−1)2

Answer 1

The given function notation \( f(n) = n^2 \) indicates that the function produces the square of the term \( n \). To find which sequence corresponds to this function, we can evaluate the function for several integer values of \( n \):

- For \( n = 1 \), \( f(1) = 1^2 = 1 \)
- For \( n = 2 \), \( f(2) = 2^2 = 4 \)
- For \( n = 3 \), \( f(3) = 3^2 = 9 \)
- For \( n = 4 \), \( f(4) = 4^2 = 16 \)
- For \( n = 5 \), \( f(5) = 5^2 = 25 \)

Putting these values together, we get the sequence: \( 1, 4, 9, 16, 25 \).

Therefore, the correct response is:

**\( a_n = 1, 4, 9, 16, 25 \dots \)**