Write a recursive formula for the sequences 2 5 11 23 9 18 3

Write a recursive formula for the sequences

2, 5, 11, 23…

9, -18, 36, -72 ...

4, 68, 314500, …

39, 9, 93, …

6. You are given following recursive function

f(n) = 2*f(n-2)-2

f(1)=2 and f(2)=3

Assume that you want to resample the first m terms of the sequence which derives from this function by skipping every second term. Given that you plot the output of the filtered recursive function (y axis for f(n) and x axis for n), calculate the plot area (filled area) under your graph for the first k terms.

7. Find the first 5 terms of the sequences and draw plots (n is your x axis, f(n) is your y axis).

f(1) = 6

f(n) = f(n-1)/2 + 4

f(1) = 2

f(2) = 4

f(n) = f(n-1)² + n*f(n-1)

f(1) = 100

f(n) is the f(n-1) decreased by 20%

f(1) = 3

f(n) = f(n-1) +5

f(1) = 3

f(n) = 2f(n-1)

Solution

5) a₁ = 5 , a_n =2 a_n-1 + 1

a₁ = 9 , a_n = (-1)^n-1 2 a_n-1

   a₁ = 4 , a_n = a_n-1³ + a_n-1