aFind a9 for the geometric sequence having a320 and a6160 bF

a.Find a₉ for the geometric sequence having: a₃=20 and a₆=160

b.Find a₅ and the general formula for n^th term, a_n for the geometric sequence: 4, -12, 36, -108, ...

Solution

a. a₃=20= a r²

a6= 160= a r⁵

From the above two equations

r³=8

r=2

a(2)²=20

a=5

a₉= 5(2)⁸= 5*256 = 1280

b. a=4, r=-12/4=-3

a₅= 4(-3)⁴= 324

a_n= a r^n-1