Respuesta :
The first five terms are 6, 3, 1.5, 0.75, 0.375
Solution:
Given that we have to find the first five terms of sequence
Given formula:
[tex]f(n) = \frac{1}{2} \times f(n-1)[/tex]
Also, given that f(0) = 12
First term:
Substitute n = 1
[tex]f(1) = \frac{1}{2} \times f(1-1)\\\\f(1) = \frac{1}{2} \times f(0)[/tex]
Substitute f(0) = 12
[tex]f(1) = \frac{1}{2} \times 12\\\\f(1) = 6[/tex]
Thus first term of sequence is 6
Second term:
Substitute n = 2
[tex]f(2) = \frac{1}{2} \times f(2-1)\\\\f(2) = \frac{1}{2} \times f(1)[/tex]
Substitute f(1) = 6
[tex]f(2) = \frac{1}{2} \times 6\\\\f(2) = 3[/tex]
Thus the second term of sequence is 3
Third term:
Substitute n = 3
[tex]f(3) = \frac{1}{2} \times f(3-1)\\\\f(3) = \frac{1}{2} \times f(2)[/tex]
Substitute f(2) = 3
[tex]f(3) = \frac{1}{2} \times 3\\\\f(3) = 1.5[/tex]
Thus the third term of sequence is 1.5
Fourth term:
Substitute n = 4
[tex]f(4) = \frac{1}{2} \times f(4-1)\\\\f(4) = \frac{1}{2} \times f(3)[/tex]
Substitute f(3) = 1.5
[tex]f(4) = \frac{1}{2} \times 1.5\\\\f(4) = 0.75[/tex]
Thus the fourth term of sequence is 0.75
Fifth term:
Substitute n = 5
[tex]f(5) = \frac{1}{2} \times f(5-1)\\\\f(5) = \frac{1}{2} \times f(4)[/tex]
Substitute f(4) = 0.75
[tex]f(5) = \frac{1}{2} \times 0.75\\\\f(5) = 0.375[/tex]
Thus the fifth term of sequence is 0.375
