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A sequence is defined by f(1)=3 and f(n)=2f(n−1) for n1. Which of the following statements defines the nth term of f? A. f(n)=3+2(n−1) for n1 B. (n)=3+2n for n1 C. f(n)=32n−1 for n1 D. f(n)=32n for n1

Respuesta :

MrRoyal

Answer:

[tex]f(n) = 3 * 2^{n-1}[/tex] for [tex]n \geq 1[/tex]

Step-by-step explanation:

Given

[tex]f(1) = 3[/tex]

[tex]f(n) =2f(n-1)[/tex]

Required

Determine f(n)

When n = 2

[tex]f(2) = 2 * f(2 -1)[/tex]

[tex]f(2) = 2 * f(1)[/tex]

[tex]f(2) = 2 * 3[/tex]

[tex]f(2) = 6[/tex]

When n = 3

[tex]f(3) = 2 * f(2)[/tex]

[tex]f(3) = 2 * 6[/tex]

[tex]f(3) = 12[/tex]

When n = 4

[tex]f(4) = 2 * f(3)[/tex]

[tex]f(4) = 2 * 12[/tex]

[tex]f(4) = 24[/tex]

List out f1 to f4

[tex]f(1) = 3 * 2^{1-1}[/tex] = 3

[tex]f(2) = 3 * 2^{2-1}[/tex] = 6

[tex]f(3) = 3 * 2^{3-1}[/tex] = 12

[tex]f(4) = 3 * 2^{4-1}[/tex] = 24

[tex]f(n) = 3 * 2^{n-1}[/tex] for [tex]n \geq 1[/tex]

abidemiokin

The nth term of the sequence is 3n

Given the recursive function expressed as:

f(n)=2f(n−1)

f(1) = 3

Get the second term:

f(2) = 2f(1)

f(2) = 2(3)

f(2) = 6

Get the third term;

f(3) = 2f(2)

f(3) = 2(6)

f(3) = 12

This form a sequence 3, 6 , 12...

The nth term of the sequence is an = a + (n-1)d

an = 3 + (n - 1)*3

an = 3+(3n-3)

an = 3 + 3n - 3

an = 3n

Hence the nth term of the sequence is 3n

Learn more on sequence here;https://brainly.com/question/18600443