Which sequence has the given function notation f(n)=n2

Question

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 function notation \( f(n) = n^2 \) defines a sequence where each term is the square of its position \( n \).

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 \( n = 5 \), \( f(5) = 5^2 = 25 \)

From the options you provided, the sequence that matches with \( f(n) = n^2 \) is:

\( a_n = 1, 4, 9, 16, 25, \ldots \)

So the correct response is: \( a_n = 1, 4, 9, 16, 25, \ldots \)