Answer:
1. 11, 17, 23, 29, 35
2. 50, 25, 12.5, 6.25, 3.125
3. 1, 6, -4, 16, -24
4. 4, 6, 9, 13, 18
Step-by-step explanation:
1. Given that [tex]a_{n + 1} = a_{n} + 6[/tex] and [tex]a_{1} = 11[/tex] for n ≥ 1
So, [tex]a_{1} = 11[/tex]
[tex]a_{2} = a_{1} + 6 = 11 + 6 = 17[/tex]
[tex]a_{3} = a_{2} + 6 = 17 + 6 = 23[/tex]
[tex]a_{4} = a_{3} + 6 = 23 + 6 = 29[/tex]
[tex]a_{5} = a_{4} + 6 = 29 + 6 = 35[/tex]
2. Given that [tex]a_{n} = a_{n - 1} \div 2[/tex] and [tex]a_{1} = 50[/tex] for n ≥ 2
So, [tex]a_{1} =50[/tex]
[tex]a_{2} = a_{1}\div 2 = 50\div 2 = 25[/tex]
[tex]a_{3} = a_{2}\div 2 = 25\div 2 = 12.5[/tex]
[tex]a_{4} = a_{3}\div 2 = 12.5\div 2 = 6.25[/tex]
[tex]a_{5} = a_{4} \div 2 = 6.25\div 2 = 3.125[/tex]
3. Given that f(n + 1) = - 2 f(n) + 8 and f(1) = 1 and n ≥ 1
Hence, f(1) = 1
f(2) = - 2 f(1) + 8 = -2 + 8 = 6
f(3) = -2 f(2) + 8 = - 12 + 8 = - 4
f(4) = - 2 f(3) + 8 = 8 + 8 = 16
f(5) = - 2 f(4) + 8 = - 32 + 8 = - 24
4. Given that f(n) = f(n - 1) + n and f(1) = 4 and n ≥ 2
Hence, f(1) = 4
f(2) = f(1) + 2 = 4 + 2 = 6
f(3) = f(2) + 3 = 6 + 3 = 9
f(4) = f(3) + 4 = 9 + 4 = 13
f(5) = f(4) + 5 = 13 + 5 = 18 (Answer)
