I need help with these. They are hard.​

Accepted Solution

Answer:Find the explicit from for the sequence [tex]t_n=t_{n-1}+4,t=6[/tex]:[tex]a_n=4n+2[/tex]This next question I edited a bit.  Your question just says find the four terms.  I'm assuming they meant the first four. I also changed the c to an [tex]a[/tex].Find the first four terms of the sequence given by: [tex]a_n=n a_{n-1}-3,a_1=2[/tex]:a) 2,1,0.-3You might want to read that second question again because there is errors in the question or things that don't really make sense.  I made my own interpretation of the problem based on my own mathematical experience.Step-by-step explanation:So your first question actually says that you can find a term by taking that term's previous term and adding 4.So more terms of the sequence starting at first term 6 is:6,10,14,18,....This is an arithmetic sequence.  When thinking of arithmetic sequences you should just really by thinking about equations of lines.Let's say we have this table for (x,y):x  |   y----------1      62    103     144     18So we already know the slope which is the common difference of an arithmetic sequence.We also know point slope form of a line is [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point on the line.  You can use any point on the line. I'm going to use the first point (1,6) with my slope=4.[tex]y-6=4(x-1)[/tex][tex]y=6+4(x-1)[/tex]    :I added 6 on both sides here.[tex]y=6+4x-4[/tex]     :I distribute here.[tex]y=4x+2[/tex]        :This is what I get after combining like terms.So [tex]a_n=y[/tex] and [tex]x=n[/tex] so you have:[tex]a_n=4n+2[/tex]---------------------------------------------------------------------------------------The first four terms of this sequence will be given by:[tex]a_1,a_2,a_3,a_4[/tex][tex]a_1=2[/tex] so it is between choice a, c, and d.[tex]a_n=na_{n-1}-3[/tex]To find [tex]a_2[/tex] replace n with 2:[tex]a_2=2a_{1}-3[/tex][tex]a_2=2(2)-3[/tex][tex]a_2=4-3[/tex][tex]a_2=1[/tex]So we have to go another further the only one that has first two terms 2,1 is choice a.