P=0.25; R=1.5; listfor(m,1, 30,P=R*P*(1-P))[THIS IS THE SIMPLE LOOP THAT GENERATES THE FOLLOWING RESULTS]:
(0.28125, 0.3032226563, 0.3169180155, 0.3247214804, 0.3289161609, 0.33109548, 0.3322068947, 0.3327682107, 0.333050293, 0.333191693, 0.3332624831, 0.3332979007, 0.3333156151, 0.3333244738, 0.3333289034, 0.3333311184, 0.3333322258, 0.3333327796, 0.3333330565, 0.3333331949, 0.3333332641, 0.3333332987, 0.333333316, 0.3333333247, 0.333333329, 0.3333333312, 0.3333333323, 0.3333333328, 0.3333333331, 0.3333333332)
As you can see, they are trending towards P=(R - 1)/R =(1.5 - 1)/1.5 =0.5/1.5 =1/3 =0.3333333......ETC.
As you can see in your question, they have given you a "formula": P(n+1) =RP(n)(1 - P(n). You would plug in the initial values given to you: P(0)=0.25 and R=1.25. This is a "recursive formula" where the first result is fed back into the formula to generate the next value, and then that is fed back into the formula to generate the next value and so on for 30 values. I simply wrote a very short computer code to calculate the values for you.
