Question
Find the 6th term of the geometric sequence with a4=256/625 and a11=-4194304/48828125
Answers
Reiny
term 4 = ar^3 = 256/625
term 11 = ar^10 = -4194304/48828125
so dividing the second by the first:
r^7 = 16384/78125
r = 4/5
so 256/625 = a(4/5)^3
a = 4/5
so term 6 = ar^5 = (4/5)(4/5)^5
= (4/5)^6 = 4096/15625
term 11 = ar^10 = -4194304/48828125
so dividing the second by the first:
r^7 = 16384/78125
r = 4/5
so 256/625 = a(4/5)^3
a = 4/5
so term 6 = ar^5 = (4/5)(4/5)^5
= (4/5)^6 = 4096/15625