TaSK $2($OF $5)$

Objectives: The student will practice different repetition structures.

Timekeeper: This task should take approximately $20$ minutes. The time estimate is only a guideline $($some teams may use less time, while others may use more$).$

Jacobsthal numbers are the defined by the recurrence relation:

$J_n=J_{n-1}+2J_{n-2}$

Where the following initial conditions are given:

$J_0=0,J_1=1$

Part A

On a separate piece of paper $($or in Excel$),$ complete the trace table below to make sure you understand how the sequence is computed.

$\backslash$table$[[$n$,$Jn$-2,$Jn$-1,$Jn$],[0,,,0],[1,,0,1],[2,0,1,],[3,,,],[4,,,],[5,,,],[6,,,]]$

Part B

Develop a MATLAB program that calculates Jacobsthal numbers to the $n^{th}$ term.

User inputs a positive, real integer value $\text{'}n\text{'}.$ Use an input command for this.

Compute the Jacobsthal sequence to the $n^{th}$ term using the recurrence equation and initial conditions given above.

The program should output the Jacobsthal sequence for the number of terms entered by the user.

Save your program as ACT MLATLAB$\_2p2b$ UCusername.m

PART C

Develop a MATLAB progiam that will prompt the user for a positive integer. The program should then generate and output the Jacobsthal sequence until the final term in the sequence is greater than or equal to the integer entered by the user. The program should also output how many terms in the Jacobsthal sequence were outputted.