Question

Help me if you can please.

Answer 1

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

Explanation:

1. Given that
`a_(n + 1) = a_(n) + 6` and
`a_(1) = 11` for n ≥ 1

So,
`a_(1) = 11`

`a_(2) = a_(1) + 6 = 11 + 6 = 17`

`a_(3) = a_(2) + 6 = 17 + 6 = 23`

`a_(4) = a_(3) + 6 = 23 + 6 = 29`

`a_(5) = a_(4) + 6 = 29 + 6 = 35`

2. Given that
`a_(n) = a_(n - 1) / 2` and
`a_(1) = 50` for n ≥ 2

So,
`a_(1) =50`

`a_(2) = a_(1)/ 2 = 50/ 2 = 25`

`a_(3) = a_(2)/ 2 = 25/ 2 = 12.5`

`a_(4) = a_(3)/ 2 = 12.5/ 2 = 6.25`

`a_(5) = a_(4) / 2 = 6.25/ 2 = 3.125`

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)