Q:

Find a4 for the arithmetic series with S4=-36 and a1=9

Accepted Solution

A:
ANSWERThe 4th term is -27EXPLANATIONThe sum of the first n-terms of an arithmetic sequence is [tex]S_n= \frac{n}{2} (2a_1+d(n-1))[/tex]It was given that,[tex]S_4 = - 36[/tex][tex]a_1 = 9[/tex][tex] - 36= \frac{ 4}{2} (2 \times 9+d(4-1))[/tex][tex]-36=2(18+3d)[/tex][tex]-18=18+3d[/tex][tex]-18 - 18 = 3d[/tex][tex] 3d = - 36[/tex][tex]d = - 12[/tex]The n-term is given by:[tex]a_n=a_1+ (n-1)d[/tex]We substitute n=4 to get,[tex]a_4=9+ (4-1) \times -12[/tex][tex]a_4=9+ 3\times -12[/tex][tex]a_4=9 - 36[/tex][tex]a_4= - 27[/tex]